Algebra 1 Worksheets | Linear Equations Worksheets - Free Printable

Let's solve each part of this worksheet step by step.

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Part 1: What is the slope of each line?

We will determine the slope of each line from the graph using the formula:

$$
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}}
$$

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#### 1)
Line goes from (-4, 3) to (2, -3)

$$
\text{Rise} = -3 - 3 = -6,\quad \text{Run} = 2 - (-4) = 6
$$
$$
\text{Slope} = \frac{-6}{6} = -1
$$

✔ Slope = -1

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#### 2)
Line goes from (-4, -1) to (4, 1)

$$
\text{Rise} = 1 - (-1) = 2,\quad \text{Run} = 4 - (-4) = 8
$$
$$
\text{Slope} = \frac{2}{8} = \frac{1}{4}
$$

✔ Slope = 1/4

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#### 3)
Line goes from (-2, 4) to (2, -4)

$$
\text{Rise} = -4 - 4 = -8,\quad \text{Run} = 2 - (-2) = 4
$$
$$
\text{Slope} = \frac{-8}{4} = -2
$$

✔ Slope = -2

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#### 4)
Line goes from (-2, -4) to (2, 4)

$$
\text{Rise} = 4 - (-4) = 8,\quad \text{Run} = 2 - (-2) = 4
$$
$$
\text{Slope} = \frac{8}{4} = 2
$$

✔ Slope = 2

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#### 5) $ y = \frac{1}{2}x - 3 $

This is in slope-intercept form: $ y = mx + b $

So, slope = $ \frac{1}{2} $

✔ Slope = 1/2

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#### 6) $ y = -\frac{2}{7}x + 1 $

Slope is the coefficient of $ x $: $ m = -\frac{2}{7} $

✔ Slope = -2/7

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#### 7) $ y = 10x + 2 $

Slope = 10

✔ Slope = 10

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#### 8) $ y = -3x $

Slope = -3

✔ Slope = -3

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✔ Summary of Slopes:

| Problem | Slope |
|--------|--------------|
| 1 | -1 |
| 2 | 1/4 |
| 3 | -2 |
| 4 | 2 |
| 5 | 1/2 |
| 6 | -2/7 |
| 7 | 10 |
| 8 | -3 |

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Part 2: Write the slope-intercept form and plot the equation

The slope-intercept form is:

$$
y = mx + b
$$
where $ m $ = slope, $ b $ = y-intercept

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#### 9)
Given:
- Slope = $ \frac{1}{7} $
- y-intercept = -2

So,
$$
y = \frac{1}{7}x - 2
$$

✔ Equation: $ y = \frac{1}{7}x - 2 $

To plot:
- Start at (0, -2) — y-intercept
- Use rise/run = 1/7 → go up 1, right 7 to get next point (7, -1)

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#### 10)
Given:
- Slope = $ -\frac{3}{4} $
- y-intercept = -3

So,
$$
y = -\frac{3}{4}x - 3
$$

✔ Equation: $ y = -\frac{3}{4}x - 3 $

To plot:
- Start at (0, -3)
- Use rise/run = -3/4 → down 3, right 4 → next point (4, -6)

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✔ Final Answers:

#### Part 1: Slopes
1) -1
2) $ \frac{1}{4} $
3) -2
4) 2
5) $ \frac{1}{2} $
6) $ -\frac{2}{7} $
7) 10
8) -3

#### Part 2: Equations
9) $ y = \frac{1}{7}x - 2 $
10) $ y = -\frac{3}{4}x - 3 $

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You can now fill these into your worksheet! Let me know if you'd like a visual sketch or explanation for plotting.