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6.1GraphingwithSlope-InterceptForm
Before we begin looking at systems of equations, let’s take a moment to review how to graph linear
equations using slope-intercept form. This will help us because one way we can solve systems of equations is to
graph the equations and see where the lines cross.
Slope-Intercept Form
Any linear equation can be written in the form 1=+< where is the slope and < is the 1-intercept.
Sometimes the equation we need to graph will already be in slope-intercept form, but if it’s not, we’ll need to
rearrange the equation to get it into slope-intercept form. Take a look at the following equations:
Example 1
1=2 − 1
This equation is already in slope-intercept form.
Nothing needs to be done.
Example 3
3 − 21 = 4
This example is also not in slope-intercept form.
We’ll first subtract 3, but then notice that we’ll be
left with a X21. Be careful because that negative
sign is important. Next divide by X2 to get 1 by
itself.
3 − 3 − 21 = 4 − 3
X21 = −3 + 4
X21
−2 =−3 + 4
−2
1=3
2 − 2
Example 2
2 + 1 = 7
This equation is not in slope-intercept form. We
need to subtract 2 from both sides to get the 1 by
itself.
2 − 2 + 1 = 7 − 2
1=X2 +7
Example 4
X4 + 21 = 8
This is not in slope-intercept form. We’ll first need
to get rid of the X4 by adding 4 and then we’ll
have to get rid of the times by 2 by dividing by 2.
That will get 1 by itself.
X4 + 4+ 21 = 8 +4
21 = 4 + 8
21
2=4 + 8
2
1=2 + 4
So, step one in graphing is to get the equation in slope-intercept form.
