Graphing Lines Using Standard Form worksheets - Free Printable

To graph each line, we need to find two points on the line — usually the x-intercept and y-intercept — then draw a straight line through them.

The standard form of a linear equation is:
Ax + By + C = 0

We can rewrite it as:
Ax + By = -C

Then:
- To find x-intercept, set y = 0 → solve for x.
- To find y-intercept, set x = 0 → solve for y.

Let’s go one by one.

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1) 6x – y + 4 = 0

Rewrite: 6x – y = -4

→ x-intercept (set y=0):
6x = -4 → x = -4/6 = -2/3 ≈ -0.67

→ y-intercept (set x=0):
–y = -4 → y = 4

Points: (-2/3, 0) and (0, 4)

Plot these and draw line.

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2) –2x – 2y – 4 = 0

Simplify first? Divide entire equation by -2:
x + y + 2 = 0 → x + y = -2

→ x-intercept (y=0): x = -2
→ y-intercept (x=0): y = -2

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

Draw line through them.

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3) –4x – y + 3 = 0

Rewrite: –4x – y = -3 → multiply both sides by -1:
4x + y = 3

→ x-intercept (y=0): 4x = 3 → x = 3/4 = 0.75
→ y-intercept (x=0): y = 3

Points: (0.75, 0) and (0, 3)

Draw line.

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4) x – y – 1 = 0

Rewrite: x – y = 1

→ x-intercept (y=0): x = 1
→ y-intercept (x=0): –y = 1 → y = -1

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

Draw line.

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5) –5x – y + 1 = 0

Rewrite: –5x – y = -1 → multiply by -1:
5x + y = 1

→ x-intercept (y=0): 5x = 1 → x = 1/5 = 0.2
→ y-intercept (x=0): y = 1

Points: (0.2, 0) and (0, 1)

Draw line.

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6) 4x – 4y – 16 = 0

Simplify: divide by 4 → x – y – 4 = 0 → x – y = 4

→ x-intercept (y=0): x = 4
→ y-intercept (x=0): –y = 4 → y = -4

Points: (4, 0) and (0, -4)

Draw line.

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All lines are now ready to be sketched using their intercepts.

Final Answer:
Graph each line using the intercepts calculated above. For example, for problem 1, plot (-2/3, 0) and (0, 4), then draw a straight line through them. Repeat similarly for problems 2–6 using their respective intercept pairs.