Graphing Lines by X and Y-Intercepts (examples, solutions, videos ... - Free Printable

Let’s solve the problem step by step.

We are given the equation:
3x + 2y = 12

We need to graph this line using x- and y-intercepts.

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Step 1: Find the x-intercept

To find the x-intercept, set y = 0 and solve for x.

So plug in y = 0:
→ 3x + 2(0) = 12
→ 3x = 12
→ x = 12 ÷ 3
→ x = 4

So the x-intercept is at point (4, 0)

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Step 2: Find the y-intercept

To find the y-intercept, set x = 0 and solve for y.

Plug in x = 0:
→ 3(0) + 2y = 12
→ 2y = 12
→ y = 12 ÷ 2
→ y = 6

So the y-intercept is at point (0, 6)

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Step 3: Plot the two points

On a coordinate grid:
- Plot (4, 0) → that’s on the x-axis, 4 units right.
- Plot (0, 6) → that’s on the y-axis, 6 units up.

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Step 4: Draw the line

Use a ruler to draw a straight line through both points. Extend it across the grid.

This line represents all solutions to the equation 3x + 2y = 12.

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Final Answer:
The x-intercept is (4, 0), the y-intercept is (0, 6). Plot these two points and draw a straight line through them to graph the equation 3x + 2y = 12.