Graphing Linear Equations In Standard Form Ax + By = C

Linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line. We will use The Standard Form of the equation to graph the line.

The formula for Standard Form is: If y is zero, we have Ax = C is the x-intercept. If x is zero, we have By = C is the y-intercept. − — is the slope. Ax + By = C ABAB Using the x-intercept and/or y-intercept as a starting point, you can use the slope to graph more points on the line of the equation. We can find 3 things just by looking at the formula: To find where the line crosses each axis, let the other value be zero.

These equations are all in Standard Form: Notice that these equations are all in the form Ax + By = C. 2x – y = -1 x + y = -4 3x – 2y = 4

1)Find the x-intercept: -1 ÷ 2 = -1/2 2) Find the y-intercept: -1 ÷ -1 = 1 3) Plot the y-intercept. 4) Find the slope: -A/B − 2/-1 = 2 5) Plot more points using the slope. up 2 right 1 up 2 right 1 2x – y = -1

right 1 down 1 up 1 left 1 1)Find the x-intercept: -4 ÷ 1 = -4 2) Find the y-intercept: -4 ÷ 1 = -4 3) Plot the x and y- intercepts. 4) Find the slope: -a/b − 1/1 = -1 5) Plot more points using the slope. x + y = -4

A graph with only one letter (x or y) only crosses that axis at that point. x = -3 ONLY crosses the x-axis… at -3 y = 5 ONLY crosses the y-axis… at 5

SUMMARY The formula for Standard Form is: If y=0, C ÷ A gives the x-intercept If x=0, C ÷ B gives the y-intercept − — is the slope Using the x-intercept and/or y-intercept as a starting point, you can use the slope to graph the line of the equation. Ax + By = C ABAB