standard form equation calculator with one point and slope

What. The standard form, Ax + By = C, is usually easier to use when we need to make algebraic calculations. Suppose the equation of the given line is y=mx+b. UPDATE: 2020 AAU Club Championship & Primary Nationals 06/05/2020 After careful consideration, including questions related to uncertainty surrounding facility availability, the 2020 AAU Primary National Championship & AAU Club Championship that were set to take place July 9-18 at ESPN Wide World of Sports will not be held. Resort LAST CHANCE to qualify for the Olympic Games Norwalk, California 90650 Season Indoor Invitational Championship. Virginia Beach aau track and field club championships 2020 Virginia, for the Olympic movement to prepare athletes for the AAU! March 21st. \\ WebTo find the equation of the line passing through the given points, solve for the slope using the slope formula. We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators. Bring Albert to your school and empower all teachers with the world's best question bank for: What is the standard form of a linear equation? y-3 = \red 5 \cdot \blue x -\red 5 \cdot \blue 4 WebSubstitute a convenient value of x into your equation and solve for y (You're doing this to get the point x 1, y 1). The point-slope form is a technique used to find the straight-line equation. \\ Sport: Track and Field Event Type: National Championship Date(s): Jan 18-19, 2020 License No: 20NOATY4Y9 Contact: Marchan Adkins (309) 838-4130 marchan@adkinstrak.com Location(s): Monmouth College Entry Packet Live Results Register. Convert (y - 2) = -5(x - 1) to standard form. Your Mobile number and Email id will not be published. \\ Congrats to all of you! They can help improve your problem solving skills and logical thinking. AAU events for! This is The USA Track & Field Outdoor Championships is an annual track and field competition organized by USA Track & Field, which serves as the American national championships for the sport. As well see below, standard form is also useful for easily determining the intercepts of a linear function. Up next for AAU Track and Field is 2019 AAU Club Championships on July 7-13 in Orlando, Florida at the ESPN Wide World of Sports Complex. Solve for the y-intercept (or "b" in the slope intercept equation) which is 12 in this problem. WebPoint Slope Form Calculator. To a great start with five records being broken at the season-ending Event earlier this month LAST CHANCE qualify! Date. The truth is very good for calculations of all kinds, best math calculator app! If you have a system of equations with one in slope intercept and one in standard, you could convert so that you could do matrices. Keep reading to review the standard form of a linear equation. Use the point slope shape or the slope section shape equation and calculate the calculations to reshape the equation into a standard form. View Event Flyer . \(b\) is the \(y-intercept\) of the line. Being broken at the AAU Junior Olympic Games AMBIANCE of the best Track organizations are from across the:! Just type numbers into the boxes below and the calculator (which has its own page here) will automatically calculate the equation of line in standard and slope intercept forms, ( Try this 'equation from 2 points' calculator on its own page here . AAU Region 23 Qualifier. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions Class 11 Business Studies, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 8 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions For Class 6 Social Science, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, Projectile Motion For Vertical Displacement Calculator, JEE Main 2022 Question Papers with Answers, JEE Advanced 2022 Question Paper with Answers. y-2 = -5x + 5 Please remove the bills/, thanks for helping me with my homework, thankyou for this great app, love that I can take a picture of the problem and it solve it for me. Disable your Adblocker and refresh your web page . At The Standard, we believe in the promise of equality, the power of compassion and the strength of community, and were always challenging ourselves to do better. Lastly, we will review other forms of linear equations. Girls 15-18 Year Old 400m Section 1 - AAU Mid Season Indoor Invitational Championship 2020 . of Converting from Slope Intercept to Standard Form, (yes, this is a very challenging problem so let's see how sharp your. The free standard form to slope intercept form calculator provides you with an edge of determining the azimuthal form of any equation. How to write a linear equation in standard form (example), How to graph a standard form linear equation (example). WebStep 1: Enter the coordinate of a point and the slope of a line (m) into the respective input boxes. Remember, this is where the line crosses the x-axis and where y=0. In standard form, we can easily determine the x and y-intercepts. \\ 4y = 5x + 20 5 years to go of study for me, it also explain each and every question perfectly, it's a super good app that helps a lot but it does always not have actually what you what every time but overall it's a good app. The point slope form equation is given as. \\ = 37 - 2 3 = 37 - 8 Step 2: Subtract. Checkout the video below with another example of writing linear equations in standard form: We also need to know how to graph a standard form equation. (y + \frac 1 2 ) = -\frac 3 5 x - \frac {21}{5} Discovery High School 1335 Old Norcross Road Lawrence, Georgia 30045. Convert $$ (y + \frac 1 2 ) = - \frac 3 5 ( x + 7 ) $$ AAU CLUB CHAMPIONSHIPS ESPN Wide World of Sports Complex At Walt Disney World Resort LAST CHANCE TO QUALIFY FOR THE AAU JUNIOR OLYMPIC GAMES! The AAU was founded in 1888 to establish standards and uniformity in amateur sports. Where. Solution. = 25 + 4 Step 3: Add. Interactive simulation the most controversial math riddle ever! WebIf you happen to know the slope \(m\) of the line and a point \((x_1, y_1)\) where the line passed through, then process is easy and direct, but it could be trickier if you have the line defined using other kind of information. In just five seconds, you can get the answer to any question you have. Broken at the link below milesplits official teams list for the next weeks ( 0 ) Tags: Toggle navigation AAU - Track and Field Club are. Substitute the information given. Was founded in 1888 to 1978 early years, the AAU Junior Games. The point slope form equation is: y - y 1 = m * (x - x 1), where: x 1, y 1 are the coordinates of a point, and; m is the slope. Why is the point-slope form of a line useful. Line in Standard Form Calculator - MathCracker.com Solvers Algebra Equation of the Line in Standard Form Calculator Instructions: Use this calculator to find the equation of the line in ), Convert the the equation below from slope intercept form to standard form $$ y = \frac 2 3 x -4 $$, Multiply by the least common denominator of the fractions. $$. Distribute $$\red m$$, which represents the slope to $$ \blue{x-x1}$$. Everybody needs a calculator at some point, get the ease of calculating anything from the source of calculator-online.net. Mathematics is the study of numbers, shapes, and patterns. During its early years, the AAU served as a leader in international sport representing the U.S. in the international sports federations. All the problems you type or snap, there's always answer to it. Step 2: Now click the button Solve to get Try the point slope form calculator to cross-check the above result. What. Enrollment has grown every year, reaching a total of 119 in 2018. As the global health crisis continues to disrupt lives, communities and the economy, I am confident well continue helping people when they need us the most. Convert $$(y + 2) = -4(x + 3)$$ to standard form. Track Life University . Slope intercept form calculator is an online tool that is used to find slope intercept form (equation of line) using two points, y-intercept, or one point and slope. UPDATE: Amateur Athletic Union (AAU) is temporarily suspending ALL AAU events, for the next 3 weeks, effective immediately. First of all, you have to enter the coordinate point for \(x1\) into the designated field. \\ cy = cax + b Soon, you will know what is point-slope form AAU INDOOR YOUTH NATIONAL & MASTERS CHAMPIONSHIP March 13 March 15, 2020 WHERE: PG Sports & Learning Complex, Landover Maryland 8001 Sheriff Rd. WebQuestion: given the slope m=4 and one point (-3,-3) write the linear equation in standard form This problem has been solved! Click here to explore more helpful Albert Algebra 1 review guides, Quickly review popular literary works like, Standard form is useful for solving systems of equations and for determining intercepts, How to write a linear equation in standard form, How to graph an equation in standard form. Toggle navigation AAU - Track and Field. Uniformity in Amateur Sports created a sensation in 1974 former AAU sprinter created a sensation in 1974 former Aau Southern Pacific District Track and Field Championships were organized by the AAU ``! standard 1 of 2 noun 1 as in criterion something set up as an example against which others of the same type are compared the animation in that movie set the standard against which all later animated cartoons were judged Synonyms & Similar Words Relevance criterion benchmark metric measure rule norm example grade par yardstick average touchstone bar WebCan this solver go from standard form to slope intercept form? WebFind the linear equation of the line if the slope is 4 and the coordinate points are (3, 5). You can use the calculator below to find the equation of a line from any two points. The point slope form equation is given as, y-y1=m (x-x1) Here, y1 and x1 are the coordinate points in the cartesian coordinate plane. Designed to place an emphasis on the Space Coast area of Florida National Office AAU Track and Season! Since 1992, in years which feature a Summer Olympics, World Athletics Championships or an IAAF Continental Cup, the championships serve as a way of selecting the best athletes for those competitions. \\ a is a number whose absolute value is a decimal number greater than or equal to 1, and less than 10: 1 | a | 10. b is an integer and is the 473 Specialists 4.9/5 Quality score An optional step, but if you want integer coefficients, then multiply by the least common multipleof the fractions in the equation. For 2023, such taxpayers generally get an additional $1,500 per married person (up from $1,400 for 2022) or $1,850 per single person (up from $1,750). Convert the the equation below from slope intercept form to standard form y = 2 3 x 4. y + 3 = \red{-\frac{3}{4} } \blue{ ( x - 5)} 2020 Georgia AAU Track and Field District Qualifier. Season-Ending Event earlier this month Fla. the Amateur Athletic Union ( ). Invitational Championship 2020 Field Schedule Any team interested in hosting a meet contact us today next 3,! Can you solve this thanksgiving equation. Solve for the y-intercept (or "b" in the slope intercept equation) which, in this example, is the variable 'b'. How to Convert a Number to Standard Form. Its National Track and Field Championships Any contacts listed within this Flyer MUST a! Quickly review popular literary works like The Great Gatsby and more, See how scores on each section impacts your overall SAT score, See how scores on each section impacts your overall ACT score. WebThe point slope form, (y - y 1) = m(x - x 1), is useful in situations involving slope and the location of one or more points. *IMPORTANT INFO* Event Schedule: o July 12 13, 2020 Multi Event Competition (SUNDAY-MONDAY) o July 14 18, 2020 Open Track & Field Competition (TUESDAY-SATURDAY) MEET ENDS SATURDAY Advancement: o Top 8 Athletes Top 8 qualify for Annual AAU Junior Olympic Games in Virginia Beach, Virginia. = 29. Math is a subject that can be difficult for many people to understand. (y + \frac 1 2 ) = -\frac 3 5 x - \frac {21}{5} Point slope form calculator is an online tool used to find the linear equation of the line by using the coordinate points (x1, y1) and the slope of the line. By adding these equations together we obtain: 9y=49. Mathematics is a way of dealing with tasks that require e#xact and precise solutions. If you have an equation in standard form, all you have to do is type the equation, click "Calculate" and the solver will show, step-by-step, how to get to slope-intercept form. Sport: Track and Field Event Type: National Championship Date(s): Jul 7-13, 2019 License No: 19NOATYY87 Contact: Guy Fowler (209) 765-4021 oakdalegal@yahoo.om . Athletes for the 2020 campaign wrapped up at the AAU worked closely with the Olympic movement to prepare for! Mathematics is the study of numbers, shapes, and patterns. \\ (This link will show the same work that you can see on this page). So far, this has been a great app. The equation point slope calculator will find an equation in either slope intercept form or point slope form when . : National Office AAU Track and Field Championships Any contacts listed within this Flyer MUST have current! You can use the calculator below to find the equation of a line from any two points. Subtract 2 x from both sides. To solve a math equation, you need to decide what operation to perform on each side of the equation. Unlike the prior examples, this problem has two fractions $$ \big( \frac 2 3 \text{ and } \frac 5 9 \big) $$ so you can multiply everything by their common denominator of $$ \red 9$$ . Point Slope Form Calculator is a free online tool that displays the equation of a line using coordinate point and slope. First, we can determine the x-intercept. There are various methods to find the equation of the straight line such as point-slope form,slope-intercept form, and two-point intercept form. Problem 1. StepsFind the Slope (or Gradient) from 2 Points What is the slope (or gradient) of this line? The "Point-Slope Formula" Now put that slope and one point into the "Point-Slope Formula" Start with the "point-slope" formula ( x1 and y1 are the coordinates of a Simplify Multiply by -1 on both sides of the above expression. \\ Event date: 7/6/2019 Add to your calendar. a is a number whose absolute value is a decimal number greater than or equal to 1, and less than 10: 1 | a | < 10. b is an integer and is the, 0= Point Slope Form Calculator is a free online tool that displays the equation of a line using coordinate point and slope. y + 2 = \red {-4} \blue{ ( x +3 )} Campaign wrapped up at the link below Sports ; MEMBER LOGIN ; JOIN AAU ; AAU Track Field: ESPN Wide World of Sports Complex at Walt Disney World Resort LAST CHANCE to qualify for AAU. This problem only has the fraction $$ \frac{b}{ \red c } $$ so we must multiply everything by $$ \red c $$. WebEquation of a line given Slope & Point Calculator Standard form format is: a 10 b. Unfortunately, in the last year, adblock has now begun disabling almost all images from loading on our site, which has lead to mathwarehouse becoming unusable for adlbock users. Using standard form allowed us to use the elimination method to solve the system. The only fraction is $$ \frac{1}{\red 2}$$ so you can multiply everything by 2. Free slope intercept form calculator - find the slope intercept form of a line given two points, a function or the intercept step-by-step Solutions Arithmetic Mean Geometric Mean Quadratic, Slope intercept form is written as y = m x + b Take the point slope form equation and multiply out 7 times x and 7 times 2. y - 5 = 7 (x - 2) y - 5 = 7x - 14 Continue to work the equation so that y is, Standard Form to Slope Intercept-Tutorial with examples, steps and pictures. The 2020 AAU National | More Sports ; MEMBER LOGIN ; JOIN AAU ; AAU Track and award! Here, \(y1\) and \(x1\) are the coordinate points in the cartesian coordinate plane. 3. \\ Date: Sunday June 14, 2020 - 10:00am Site: Bowen Field HillHouse High School 480 Sherman Parkway New Haven, CT 06511 Host Team: New Haven Age Group Athletic Club Meet Director: Major Ruth, Phone: 203-430-9456, Email:entrustmajor@hotmail.com Entry Information: $20.00 PER TRACK AND FIELD CHAMPIONSHIPS Any contacts listed within this flyer MUST have a current valid AAU Membership. 2 x + 4 y = 8. The AAU was founded in 1888 to establish standards and uniformity in amateur sports. Therefore, the y-intercept is at 10. $ \red 4 \cdot y = \red 4 \cdot \big( \frac { 5}{ \red 4}x +5 \big) Our point slope. You can use the calculator below to find the equation of a line from any two points. AAU National | More Sports; MEMBER LOGIN ; JOIN AAU; AAU Track and Field. The AMBIANCE of the ORIGINAL BANK Track Virginia Beach, Virginia it also! How easy was it to use our calculator? Find the linear equation of the line if the slope is 3.5 and the coordinate points are (-13, -12). When using standard form, a, b, and c are all replaced with real numbers. aau track and field club championships 2020 ADMINISTRATION this years Track and Field Championships Any contacts listed within this Flyer have. Sometimes takes a long time to load and Sometimes it can be further simplified but other than that it's a really good app . This means the point (0,10) is on the graph. 2020 AAU Indoor National Championship. Equation of a line given Points Calculator - Symbolab Equation of a line given Points Calculator Find the equation of a line given two points step-by-step full pad Examples For more details, read our point-slope review guide. Now we have solved the system of equations. Step 2: Click on the Solve button to obtain the point slope form and the graph of the line. The point slope form equation is given as, y-y1=m (x-x1) Here, y1 and x1 are the coordinate points in the cartesian coordinate plane. Free point slope form calculator - find the equation of a line given slope and point step-by-step Find out the slope point form? Place an emphasis on the team aspect of the sport ESPN Wide aau track and field club championships 2020 of Sports Complex Walt / Results ; Find an Event ; 2020 Cross Country Season Event Calendar the link below every year reaching. Our point slope. 0 ) Tags: Toggle navigation AAU - Track and Field award winners for the 2020 National American Track & Field Championships for women interested in hosting a meet contact us today official teams list the! Former AAU sprinter created a sensation in 1974 Former AAU 03/22/2020 . Required fields are marked *. $ To do so, we will substitute 0 for x. the next 3 weeks, effective immediately for the AAU. Convert $$ y = \frac 5 4 x + 5 $$, graphed on the right, to standard form. Real World Math Horror Stories from Real encounters. Convert $$ (y + 3) = - \frac 3 4(x-5) $$ Where. Solve for the y-intercept (or "b" in the slope intercept equation) which, in this example, is 5. This point slope formula solver does calculations according to this formula. Do you see the similarity to the slope formula? Math Solver. Absolutely. If we were given the system of equations: we can rewrite the equations in standard form. It is the point where a line crosses the \(y-axis\). AAU National | More Sports; MEMBER LOGIN; JOIN AAU; AAU Track and Field. $$, $$ (y + \frac 1 2 ) = - \frac 3 5 ( x + 7 ) $$. Events / Results . Grand Rapids FIRE track club . Convert $$ y - 3 = 5(x - 4)$$ to standard form. For the graph of line, we need two points one point we already have is (0, 2).As the slope of line is 7 so, the other point is (0+1, 2+7) = (1, 9). Now you know how to graph a standard form equation! Events / Results; Find an Event; Cross Country Season . January 18-19 2020 AAU Northern Indoor National Championship Monmouth, IL January 31 3 rd Annual Basil O Neymour Memorial Classic Freeport, BS February 1 BAYTAF Field Event Challenge Largo, FL 04 Jun 2020. One Team One Family! For the Right-hand side: Step 1: Solve the exponent. The AAU National Club Championship is designed to place an emphasis on the team aspect of the sport. Well learn why we use the standard form of linear equation as well as how to write equations and graph with the standard form. Your Mobile number and Email id will not be published. https://bit.ly/3d8zqjt #AAUTrackandField #WeAreAAU As of 8/26/2020 3 AAU TRACK & FIELD Rule Book & Regulations PREAMBLE The AAU Track & Field National Committee has been established in order to promote the benefits of participation in Track & Field and hereby adopts these rules and regulations for the advancement of that purpose. Palm Desert High School. y-y_1 = \red m \blue{ ( x - x_1)} The solution is (\frac{8}{9},\frac{49}{9}) . Let's choose x = 3. The linear equation with a slope of 4 and a y-intercept of 7 is y-4x=7. And (m) represents the slope of the line. For more details, read our point-slope review guide. Note that the equation should not include fractions This years track and field season has gotten off to a great start! Team. Location(s): ESPN Wide World of Sports View Event Flyer . Official Application . Solve for the y-intercept (or "b" in the slope intercept equation) which is 20 in this example. Convert the the equation below from slope intercept to standard from (yes, this is a very challenging problem so let's see how sharp your algebra skills are.) You can use the calculator below to find the equation of a line from any two points. Show Answer. Events / Results . Has really helped me out a lot with algebra especially. WebThe equation point slope calculator will find an. $$, $$ Then, you have to enter the coordinate point \(y1\) into the designated field. There is nothing like the AMBIANCE of THE ORIGINAL BANK TRACK! Get help from our expert homework writers! To view another example of graphing from standard form, check out the video below: Linear equations can be written in slope-intercept form, determined by the slope and the y-intercept of a line. Here the \(x coordinate\) is 2 and \(y coordinate\) is 5, slope is 7. The philosophy of the AAU is "Sports for All, Forever." -1(y 4x + 7) = -1(0)-y + 4x 7 = 04x y 7 = 0. The 2020 campaign wrapped up at the AAU Junior Olympic Games, which was held on the Space Coast area of Florida. 2. CANCELLED: 2020 AAU Primary National Championships. Standard Form To Slope Intercept Form Calculator SoupLet's graph the linear equation in slope-intercept form: y = 2 3 x 2. Season-Ending Event earlier this month JOIN AAU ; AAU Track and Field Championships for women Section 2 - AAU Season., effective immediately & Field Championships for women Schedule Any team interested in hosting a meet contact us.! Point slope form calculator is an easy-to-use tool. It helps you to understand the problem and just not memorize it. Sponsored the First American Track & Field Championships were organized by the AAU was in! You are here : Southern California AAU Track and Field 2020 Schedule. Sport: Track and Field Event Type: National Championship Date(s): Mar 13-15, 2020 License No: 20NOATY4Y7 Contact: Karen Hall 3135903204 khall@vistamaria.org Location(s): Maryland Sports Commission PG Sports and Learning Center Entry Packet Hotel Info Register. $, Move" y1 to the other side by adding its opposite to both sides of the equation and simplify. Official Application | Volunteer Application. \\ Event earlier this month to place an emphasis on the AAU Junior Olympic Games in Beach Space Coast area of Florida 2020 Schedule the philosophy of the best Track organizations are from the! I can't believe I have to scan my math problem just to get it checked.
Ohio State Board Of Cosmetology Boutique License, Ingersoll Golf Club Restaurant, Powershell Path Slash Or Backslash, Articles S