Graphing Lines Slope-Intercept Form Worksheet - Free Printable

Let’s solve each problem one by one. We’re graphing lines using slope-intercept form, which is y = mx + b, where:

- m is the slope (rise over run)
- b is the y-intercept (where the line crosses the y-axis)

We’ll find two points for each line and draw a straight line through them.

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1) y = -8x - 4

This is already in slope-intercept form.

- Slope (m) = -8 → that means go down 8, right 1 (or up 8, left 1)
- Y-intercept (b) = -4 → start at point (0, -4)

From (0, -4), move down 8 and right 1 → new point: (1, -12) — but that’s off the grid! So let’s pick another way.

Try x = -1:
→ y = -8(-1) - 4 = 8 - 4 = 4 → point (-1, 4)

So we have two points:
(0, -4) and (-1, 4)

Plot those and draw the line.

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2) y = -x + 5

Slope = -1 → down 1, right 1
Y-intercept = 5 → start at (0, 5)

From (0, 5), go down 1, right 1 → (1, 4)
Or go up 1, left 1 → (-1, 6) — also fine.

Points: (0, 5) and (1, 4)

Draw line through them.

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3) y = 2x

This is y = 2x + 0 → so y-intercept is 0 → starts at (0, 0)

Slope = 2 → up 2, right 1

From (0, 0) → (1, 2)

Also try x = -1 → y = 2(-1) = -2 → (-1, -2)

Points: (0, 0), (1, 2), (-1, -2)

Draw line through origin with steep upward slope.

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4) x = -4

This is a vertical line! Not in slope-intercept form.

It means no matter what y is, x is always -4.

So plot points like: (-4, 0), (-4, 1), (-4, -3), etc.

Draw a straight vertical line at x = -4.

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5) y = (3/2)x + 3

Slope = 3/2 → up 3, right 2
Y-intercept = 3 → start at (0, 3)

From (0, 3):
→ up 3, right 2 → (2, 6)
→ or down 3, left 2 → (-2, 0)

Check: if x = -2 → y = (3/2)(-2) + 3 = -3 + 3 = 0 → yes, (-2, 0)

Points: (0, 3), (2, 6), (-2, 0)

Draw line through them.

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6) y = (1/5)x - 4

Slope = 1/5 → up 1, right 5
Y-intercept = -4 → start at (0, -4)

From (0, -4):
→ up 1, right 5 → (5, -3)
→ or down 1, left 5 → (-5, -5)

Check: x = 5 → y = (1/5)(5) - 4 = 1 - 4 = -3 → correct
x = -5 → y = (1/5)(-5) - 4 = -1 - 4 = -5 → correct

Points: (0, -4), (5, -3), (-5, -5)

Draw line — it will be very flat since slope is small.

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✔ All problems solved step by step. Now here are the final answers as graphs described by key points to plot.

Final Answer:
1) Plot (0, -4) and (-1, 4); draw line.
2) Plot (0, 5) and (1, 4); draw line.
3) Plot (0, 0), (1, 2), (-1, -2); draw line.
4) Draw vertical line at x = -4.
5) Plot (0, 3), (2, 6), (-2, 0); draw line.
6) Plot (0, -4), (5, -3), (-5, -5); draw line.