Pre-Algebra Worksheets | Linear Functions Worksheets - Free Printable

The image you've uploaded is a worksheet titled "Sketch the Graph of Each Line" from Math-Aids.Com, which contains 8 linear equations in slope-intercept form:
$$
y = mx + b
$$
where:
- $ m $ is the slope
- $ b $ is the y-intercept

Each problem provides a graph and asks you to:
1. Identify the slope and y-intercept.
2. Sketch the line on the coordinate plane.

Let’s go through each one, verify the given answers, and explain how to sketch the graphs correctly.

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🔹 General Steps to Graph a Line:

1. Plot the y-intercept: This is the point where the line crosses the y-axis (i.e., at $ x = 0 $).
2. Use the slope to find another point:
- Slope $ m = \frac{\text{rise}}{\text{run}} $
- From the y-intercept, move up/down (rise) and left/right (run) accordingly.
3. Draw a straight line through both points.

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✔ Problem-by-Problem Analysis

#### 1) $ y = \frac{8}{3}x - 5 $
- Slope: $ \frac{8}{3} $
- Y-intercept: $ -5 $ → Point: $ (0, -5) $
- Explanation: Start at $ (0, -5) $. Move up 8 units, right 3 units → next point: $ (3, 3) $. Draw line through these.

✔ Correctly labeled.

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#### 2) $ y = -\frac{2}{5}x - 2 $
- Slope: $ -\frac{2}{5} $
- Y-intercept: $ -2 $ → Point: $ (0, -2) $
- Explanation: Start at $ (0, -2) $. Move down 2, right 5 → next point: $ (5, -4) $

✔ Correct.

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#### 3) $ y = \frac{3}{2}x + 3 $
- Slope: $ \frac{3}{2} $
- Y-intercept: $ 3 $ → Point: $ (0, 3) $
- Explanation: From $ (0, 3) $, up 3, right 2 → $ (2, 6) $

✔ Correct.

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#### 4) $ y = \frac{7}{4}x - 3 $
- Slope: $ \frac{7}{4} $
- Y-intercept: $ -3 $ → Point: $ (0, -3) $
- Explanation: From $ (0, -3) $, up 7, right 4 → $ (4, 4) $

✔ Correct.

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#### 5) $ y = \frac{1}{2}x + 3 $
- Slope: $ \frac{1}{2} $
- Y-intercept: $ 3 $ → Point: $ (0, 3) $
- Explanation: From $ (0, 3) $, up 1, right 2 → $ (2, 4) $

✔ Correct.

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#### 6) $ y = -3x - 3 $
- Slope: $ -3 = \frac{-3}{1} $
- Y-intercept: $ -3 $ → Point: $ (0, -3) $
- Explanation: From $ (0, -3) $, down 3, right 1 → $ (1, -6) $

✔ Correct.

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#### 7) $ y = -x + 4 $
- Slope: $ -1 = \frac{-1}{1} $
- Y-intercept: $ 4 $ → Point: $ (0, 4) $
- Explanation: From $ (0, 4) $, down 1, right 1 → $ (1, 3) $

✔ Correct.

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#### 8) $ y = 3x + 2 $
- Slope: $ 3 = \frac{3}{1} $
- Y-intercept: $ 2 $ → Point: $ (0, 2) $
- Explanation: From $ (0, 2) $, up 3, right 1 → $ (1, 5) $

✔ Correct.

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📌 Summary of All Answers:

| Problem | Equation | Slope | Y-intercept |
|--------|--------------------|-----------|-------------|
| 1 | $ y = \frac{8}{3}x - 5 $ | $ \frac{8}{3} $ | $ -5 $ |
| 2 | $ y = -\frac{2}{5}x - 2 $ | $ -\frac{2}{5} $ | $ -2 $ |
| 3 | $ y = \frac{3}{2}x + 3 $ | $ \frac{3}{2} $ | $ 3 $ |
| 4 | $ y = \frac{7}{4}x - 3 $ | $ \frac{7}{4} $ | $ -3 $ |
| 5 | $ y = \frac{1}{2}x + 3 $ | $ \frac{1}{2} $ | $ 3 $ |
| 6 | $ y = -3x - 3 $ | $ -3 $ | $ -3 $ |
| 7 | $ y = -x + 4 $ | $ -1 $ | $ 4 $ |
| 8 | $ y = 3x + 2 $ | $ 3 $ | $ 2 $ |

All values are correctly filled in on the worksheet.

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✔ Final Answer:

> The worksheet has been completed correctly. For each equation:
> - The slope and y-intercept are accurately identified.
> - The graphs are properly sketched based on those values.
>
> To sketch any line:
> 1. Plot the y-intercept.
> 2. Use rise/run of the slope to find a second point.
> 3. Draw a line through both points.

Let me know if you'd like a visual explanation or digital version of the graphs!