Worksheet on finding x- and y-intercepts of linear equations.

Explanation:
We are asked to find the x-intercept and y-intercept of three linear equations.

Recall:
- The x-intercept is where the line crosses the x-axis → that’s when y = 0.
So, plug in y = 0 into the equation and solve for x.
- The y-intercept is where the line crosses the y-axis → that’s when x = 0.
So, plug in x = 0 into the equation and solve for y.

Let’s do each one step by step.

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1. Equation: $ y = -x + 5 $

- x-intercept: Set $ y = 0 $
$ 0 = -x + 5 $
Add $ x $ to both sides: $ x = 5 $
✔ x-int = 5

- y-intercept: Set $ x = 0 $
$ y = -(0) + 5 = 5 $
✔ y-int = 5

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2. Equation: $ y = \frac{1}{2}x - 8 $

- x-intercept: Set $ y = 0 $
$ 0 = \frac{1}{2}x - 8 $
Add 8: $ \frac{1}{2}x = 8 $
Multiply both sides by 2: $ x = 16 $
✔ x-int = 16

- y-intercept: Set $ x = 0 $
$ y = \frac{1}{2}(0) - 8 = -8 $
✔ y-int = –8

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3. Equation: $ y = -\frac{4}{3}x + 2 $

- x-intercept: Set $ y = 0 $
$ 0 = -\frac{4}{3}x + 2 $
Subtract 2: $ -\frac{4}{3}x = -2 $
Multiply both sides by $ -1 $: $ \frac{4}{3}x = 2 $
Multiply both sides by $ \frac{3}{4} $:
$ x = 2 \cdot \frac{3}{4} = \frac{6}{4} = \frac{3}{2} $
✔ x-int = $ \frac{3}{2} $ (or 1.5)

- y-intercept: Set $ x = 0 $
$ y = -\frac{4}{3}(0) + 2 = 2 $
✔ y-int = 2

Double-check all steps — they’re correct.

Final Answer:
1. x-int: 5, y-int: 5
2. x-int: 16, y-int: –8
3. x-int: 3/2, y-int: 2