Graphing Linear Equations Worksheets with Answer Key - Free Printable

Let’s solve each problem one by one. We’ll graph each equation on its coordinate plane. Since we can’t draw here, I’ll tell you exactly how to draw each line — what points to plot and what the line looks like.

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Problem 1: y = -4

This is a horizontal line. No matter what x is, y is always -4.

→ Plot any two points where y = -4, for example:
- (0, -4)
- (3, -4)

Draw a straight horizontal line through them.

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Problem 2: y = 2x + 3

This is in slope-intercept form (y = mx + b), where m = 2 (slope) and b = 3 (y-intercept).

Step 1: Start at the y-intercept → (0, 3)

Step 2: Use slope = 2/1 → rise 2, run 1
From (0, 3), go up 2 and right 1 → (1, 5)

Plot those two points and draw the line.

You can also check another point: if x = -1, y = 2(-1)+3 = 1 → (-1, 1)

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Problem 3: x + y = 6

Let’s rewrite it as y = -x + 6 to make it easier.

Slope = -1, y-intercept = 6

Start at (0, 6)

Use slope -1/1 → down 1, right 1 → (1, 5)

Or find intercepts:

When x = 0 → y = 6 → (0, 6)

When y = 0 → x = 6 → (6, 0)

Plot (0,6) and (6,0), draw the line.

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Problem 4: y = (1/2)x - 5

Slope = 1/2, y-intercept = -5

Start at (0, -5)

Go up 1, right 2 → (2, -4)

Another point: from (0,-5), go up 1, right 2 again → (4, -3)

Plot (0,-5) and (2,-4), draw the line.

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Problem 5: x = 4

This is a vertical line. No matter what y is, x is always 4.

→ Plot any two points where x = 4, for example:
- (4, 0)
- (4, 3)

Draw a straight vertical line through them.

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Problem 6: y = (1/4)x + 3y

Wait — this looks wrong. Let’s fix it.

We have:
y = (1/4)x + 3y

Subtract 3y from both sides:
y - 3y = (1/4)x
-2y = (1/4)x

Now divide both sides by -2:
y = -(1/8)x

So the correct equation is: y = -¹⁄₈ x

That’s a line through the origin with slope -1/8.

Start at (0, 0)

Slope = -1/8 → down 1, right 8 → (8, -1)

But our grid only goes to x=6, so let’s pick smaller steps.

Try x = 8? Too big. Try x = 4 → y = -0.5 → (4, -0.5)

x = -8 → y = 1 → but again, out of range.

Better: use multiples of 8 within range? Not really. So just plot (0,0) and maybe (8,-1) even if it’s off-grid — or approximate.

Actually, since slope is very small, the line will be almost flat, going slightly downward.

Plot (0,0) and (8,-1) — if your graph allows, extend a bit. Or use (4, -0.5) and (-4, 0.5)

Yes! That works:

If x = 4 → y = -0.5 → (4, -0.5)

If x = -4 → y = 0.5 → (-4, 0.5)

Plot those two points and draw the line through them.

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Final Answer:

Here’s how to graph each equation:

① y = -4 → Horizontal line through y = -4 (e.g., points (0,-4), (3,-4))

② y = 2x + 3 → Line through (0,3) and (1,5)

③ x + y = 6 → Line through (0,6) and (6,0)

④ y = ½x - 5 → Line through (0,-5) and (2,-4)

⑤ x = 4 → Vertical line through x = 4 (e.g., points (4,0), (4,3))

⑥ y = ¼x + 3y → Simplifies to y = -¹⁄₈x → Line through (0,0) and (4, -0.5) or (-4, 0.5)