Graphing from Standard Form

STANDARD FORM

Standard form of the equation of a line looks like this:

Ax + By = C
We want A, B, and C to be whole numbers, and we want A to be positive.

We can graph from standard form by using the x- and y-intercepts.


INTERCEPTS

The x-intercept is where the line crosses the x-axis.
The y-intercept is where the line crosses the y-axis.

Note that at the x-intercept, y is zero. (We haven't moved up or down from the x-axis.)
At the y-intercept, x is zero. (We haven't moved right or left from the y-axis.)


GRAPHING FROM STANDARD FORM

Ex: 3x-4y=12

To find the x-intercept, we plug in 0 for y.

3x-4(0)-12 ..........................4(0) becomes 0
3x=12 ................................ now divide both sides by 3
x=4

So 4 is the x-intercept.

To find the y-intercept, we plug in zero for x.

3(0)-4x-12 ..........................3(0) becomes 0
-4x=12 ................................now divide both sides by -4
x=-3

So -3 is the y-intercept.

Graph the two intercepts and draw a line through them.