Archimedes

**__Welcome to the Archimedes page!__** ~ ~ The Archimedes Team: Kurt M, Taylor S, Skyler S, and David F.

==We will be working on using, graphing, explaining, and understanding Standard Form (Ax + By = C). ==

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Learn this, it's very important --> Ax + By = C! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

 Standard Form is using an equation in the form of Ax + By = C to form a line on a graph. There are three ways to do this: 1, you can change the problem to "y = bx + c" and then graph; 2, substitute two different values for "x" or "y" and then graph them; or 3, find the x- and y-intercepts of the line and then graph. The most used method is the third, to find the x- and y-intercepts (personally, we think it's the easiest, too). However, if "C" is zero, then method 3 does not work. You would need to also find the slope of the line you are graphing. To solve in Standard Form using the third method, you must substitute both "x" and "y" for 0 as they would be at the intercepts of the "x" and "y" axis. Once you have solved for what "x" is when "y = 0" and what "y" is when "x = 0", you can plot the x- and y-intercept of the line. Finally, you can connect the two intercepts to create the line from your equation. Problem solved!

 Here is an example of solving the first half of a Standard Form problem; Example 1: 2x + 5y = 10 2(0) + 5y = 10 ~ ~ ~ 2x + 5(0) = 10 5y = 10 ~ ~ ~ 2x = 10 5y/5 = 10/5 ~ ~ ~ 2x/2 = 10/2 y = 2 ~ ~ ~ x = 5 Now that you know that x = 5 at the x-intercept and that y = 2 at the y-intercept, you can graph the points of (5, 0) and (0, 2) and use a straight edge to connect the two points!

As you can see, we graphed the point of (5,0), which was the x-axis intercept, and the point (0,2), which was the y-axis intercept, and simply connected the dots! It's THAT easy! Problem solved!

 Lets try another one!

Example 2: 25x + 10y = 100 25(0) + 10y = 100 ~ ~ ~ 25x + 10(0) = 100 10y = 100 ~ ~ ~ 25x = 100 10y/10 = 100/10 ~ ~ ~ 25x/25 = 100/25 y = 10 ~ ~ ~ x = 4 Now that you know that x = 4 on the x-intercept and y = 2 on the y-intercept, you can graph the points of (4, 0) and (0, 10) and use a straight edge to connect the two points!

As you can see we graphed the point of (4,0), which was the x-axis intercept, and the point (0,10), which was the y-axis intercept, and simply connected the dots! It's THAT easy! Problem solved!

 Let's recap: 1.) Find your "Ax + By = C" equation. 2.) Substitute "0" for "x" and "y" separately. 3.) Solve to find the x- and y-intercepts. 4.) Plot those coordinates on a graph. 5.) Finally, connect the points and you have graphed using Standard Form!

 If you are having any trouble understanding the use of Standard Form in graphing, try these links; [] []

Vocabulary Time!
standard form: A common form of a linear equation in the form of "Ax+By=C". x-intercept: The point at which a line crosses the x-axis on a graph. y-intercept: The point at which a line crosses the y-axis on a graph.

 Here's are some videos that are helpful when it comes to graphing using standard form:

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Make sure that you look at other related videos that are shown after the TeacherTube clip!

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