Graphing Linear Equations In Standard Form Ax + By = C

of the equation to graph the line. 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.

Ax + By = C The formula for Standard Form is: 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. 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. A B 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.

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

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

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

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

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