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
Example 2
1 = 2 − 1
2 + 1 = 7
This equation is already in slope-intercept form.
Nothing needs to be done.
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 = −2 . 7
Example 3
Example 4
3 − 21 = 4
−4 + 21 = 8
This example is also not in slope-intercept form.
We’ll first subtract 3, but then notice that we’ll be
left with a −21. Be careful because that negative
sign is important. Next divide by −2 to get 1 by
itself.
This is not in slope-intercept form. We’ll first need
to get rid of the −4 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.
3 − 3 − 21 = 4 − 3
−4 + 4 + 21 = 8 + 4
−21 = −3 + 4
21 = 4 + 8
−21 −3 + 4
=
−2
−2
21 4 + 8
=
2
2
3
1 = −2
2
So, step one in graphing is to get the equation in slope-intercept form.
218
1 = 2 + 4
The p-Intercept and the Slope
Once you have an equation in slope-intercept form, start by graphing the 1-intercept on the coordinate
plane. From the 1-intercept, move the rise and run of the slope to plot another point. Finally, draw the line that
connects the two points. Let’s use our previous equations to graph step-by-step.
Example 1
1 = 2 V 1
Step 1
The 1-intercept is −1, so we
plot a point at V1 on the
1-axis to begin.
Step 2
Next, the slope is 2 which
means a rise of 2 and a run of 1.
So we’ll move up two and right
one to plot the next point.
Step 3
Finally, connect the dots with a
line. This completes the graph
of our linear function.
Up two and right one
from the 1-intercept
1-intercept of −1
Here are the rest of the examples graphed.
Example 2
Example 3
1 = −2 . 7
1 V 2
Down two,
right one
1-intercept
Example 4
1 2 . 4
1-intercept
1-intercept
Up two,
right one
Up three,
right two
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Lesson 6.1
Identify the slope as a fraction and the “-intercept of each equation. Then graph on the coordinate plane.
1. 1 = 2 . 1
2. 1 3 V 4
3. 1 . 5
Slope:
Slope:
Slope:
1-int:
1-int:
1-int:
4. 1 7
5. 1 V3 V 2
6. 1 V . 5
Slope:
Slope:
Slope:
1-int:
1-int:
1-int:
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7. 1 V 2
8. 1 V V 1
9. 1 V4
Slope:
Slope:
Slope:
1-int:
1-int:
1-int:
10. 2
Hint: This is not a function!
Slope:
11. V6
Hint: This is not a function!
Slope:
12. 1 4 V 5
Slope:
1-int:
1-int:
1-int:
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Put the following equations in slope-intercept form and then graph them on the coordinate plane.
13. 2 . 1 2
14. V3 . 1 4
15. 4 . 1 V5
16. 4 . 21 6
17. V6 . 31 V9
18. . 31 6
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19. V2 . 31 12
20. 4 V 21 8
21. V2 V 31 V9
22. V2 . 1 4
23. 6 . 21 V8
24. 2 V 31 9
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