Algebra 2 worksheet on writing and graphing equations of lines, including identifying slope and y-intercept and writing equations from graphs.

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

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Objective:

To graph and write an equation given the slope and y-intercept.
We will use the slope-intercept form of a line:
$$
y = mx + b
$$
where:
- $ m $ is the slope
- $ b $ is the y-intercept

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## Questions 1–6: Identify the slope and y-intercept

1. $ y = 5x - 1 $

- Slope ($ m $): 5
- y-int ($ b $): -1

2. $ y = -3x $

- Slope: -3
- y-int: 0 (since there’s no constant term)

3. $ y = x - 4 $

- Slope: 1 (coefficient of $ x $)
- y-int: -4

4. $ y = 7 - \frac{1}{3}x $

Rewrite as: $ y = -\frac{1}{3}x + 7 $
- Slope: $-\frac{1}{3}$
- y-int: 7

5. $ y = -x $

Same as $ y = -1x + 0 $
- Slope: -1
- y-int: 0

6. $ y = \frac{4}{3} - 8x $

Rewrite: $ y = -8x + \frac{4}{3} $
- Slope: -8
- y-int: $ \frac{4}{3} $

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## Question 7: Write the equation of the given graph

Look at the first graph (left):

- The line crosses the y-axis at (0, -3) → y-intercept = -3
- Find slope using two points:
- From (0, -3) to (1, -1): rise = $-1 - (-3) = 2$, run = $1 - 0 = 1$
- So slope = $ \frac{2}{1} = 2 $

So equation:
$$
y = 2x - 3
$$

✔ This matches one of the jumbled answers.

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## Question 8: Write the equation of the second graph

Second graph (right):

- Crosses y-axis at (0, 3) → y-intercept = 3
- Find slope using two points:
- From (0, 3) to (4, 0): rise = $0 - 3 = -3$, run = $4 - 0 = 4$
- Slope = $ \frac{-3}{4} = -\frac{3}{4} $

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

This also matches one of the jumbled answers.

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## ✔ Final Answers:

Questions 1–6:

| Problem | Slope | y-int |
|--------|-------|--------|
| 1. $ y = 5x - 1 $ | 5 | -1 |
| 2. $ y = -3x $ | -3 | 0 |
| 3. $ y = x - 4 $ | 1 | -4 |
| 4. $ y = 7 - \frac{1}{3}x $ | $-\frac{1}{3}$ | 7 |
| 5. $ y = -x $ | -1 | 0 |
| 6. $ y = \frac{4}{3} - 8x $ | -8 | $ \frac{4}{3} $ |

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Question 7:

Equation: $ \boxed{y = 2x - 3} $

Question 8:

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

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These match the jumbled answers provided at the bottom.

✔ All correct!