2.4 Writing Linear Equations Practice | PDF | Algebra | Teaching ... - Free Printable

It looks like you're trying to solve a set of algebra problems from a worksheet, but the image is not fully visible or readable. However, I can help you solve the problems based on what's typically found in such worksheets.

Let me go through the problems that are partially visible and explain how to solve them step by step.

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Problem 3:

Write an equation in slope-intercept form for each graph.

This requires identifying the slope (m) and y-intercept (b) from the graph and writing the equation in the form:

\[
y = mx + b
\]

But since we don't have the actual graphs, we’ll skip this unless you can describe them.

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Problem 4:

Write an equation in slope-intercept form for each graph.

Same as above — needs the graph.

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Problems 9–17: Write an equation in slope-intercept form for the line that satisfies each set of conditions.

Let’s solve these one by one.

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#### 9. slope = –5, passes through (0, –4)

We know:
- Slope \( m = -5 \)
- The point \( (0, -4) \) is the y-intercept because x = 0.

So, directly:
\[
y = -5x - 4
\]

✔ Answer: \( y = -5x - 4 \)

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#### 10. slope = 2, passes through (10, –3)

Use point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Plug in \( m = 2 \), \( x_1 = 10 \), \( y_1 = -3 \):
\[
y - (-3) = 2(x - 10)
\]
\[
y + 3 = 2x - 20
\]
\[
y = 2x - 23
\]

✔ Answer: \( y = 2x - 23 \)

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#### 11. slope = 1/2, passes through (0, –10)

Again, (0, –10) is the y-intercept → \( b = -10 \)

So:
\[
y = \frac{1}{2}x - 10
\]

✔ Answer: \( y = \frac{1}{2}x - 10 \)

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#### 12. slope = –2/3, passes through (6, –6)

Use point-slope:
\[
y - (-6) = -\frac{2}{3}(x - 6)
\]
\[
y + 6 = -\frac{2}{3}x + 4
\]
\[
y = -\frac{2}{3}x - 2
\]

✔ Answer: \( y = -\frac{2}{3}x - 2 \)

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#### 13. parallel to \( y = 4x + 3 \), passes through (0, –6)

Parallel lines have the same slope.

Slope of given line: \( m = 4 \)

Passes through (0, –6) → y-intercept is –6

So:
\[
y = 4x - 6
\]

✔ Answer: \( y = 4x - 6 \)

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#### 14. slope = –1, y-intercept = –5

Directly:
\[
y = -x - 5
\]

✔ Answer: \( y = -x - 5 \)

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#### 15. perpendicular to \( y = 3x - 7 \), passes through (0, –1)

Perpendicular lines have slopes that are negative reciprocals.

Given slope = 3 → perpendicular slope = \( -\frac{1}{3} \)

Point: (0, –1) → y-intercept = –1

So:
\[
y = -\frac{1}{3}x - 1
\]

✔ Answer: \( y = -\frac{1}{3}x - 1 \)

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#### 16. perpendicular to \( y = \frac{1}{2}x + 4 \), passes through (1, –7)

Slope of given line: \( \frac{1}{2} \)

Perpendicular slope: \( -2 \)

Now use point-slope:
\[
y - (-7) = -2(x - 1)
\]
\[
y + 7 = -2x + 2
\]
\[
y = -2x - 5
\]

✔ Answer: \( y = -2x - 5 \)

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#### 17. parallel to \( y = \frac{1}{2}x + 10 \), passes through (0, 4)

Same slope: \( \frac{1}{2} \)

Y-intercept is 4 → so:
\[
y = \frac{1}{2}x + 4
\]

✔ Answer: \( y = \frac{1}{2}x + 4 \)

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RESEARCHER Problem (Bonus):

> The surface of Grand Lake is at an elevation of 640 feet. During the same drought, the water level is dropping at a rate of 3 inches per day. If this trend continues, write an equation that gives the elevation in feet of the surface of Grand Lake after \( x \) days.

Step-by-step:

- Initial elevation: 640 ft
- Rate of change: 3 inches per day → convert to feet:
\( 3 \text{ inches} = \frac{3}{12} = 0.25 \text{ feet per day} \)
- Since it's dropping, slope is negative: \( m = -0.25 \)

So:
\[
y = -0.25x + 640
\]

Where:
- \( y \) = elevation in feet
- \( x \) = number of days

✔ Answer: \( y = -0.25x + 640 \)

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Summary of Answers:

| Problem | Answer |
|--------|--------|
| 9 | \( y = -5x - 4 \) |
| 10 | \( y = 2x - 23 \) |
| 11 | \( y = \frac{1}{2}x - 10 \) |
| 12 | \( y = -\frac{2}{3}x - 2 \) |
| 13 | \( y = 4x - 6 \) |
| 14 | \( y = -x - 5 \) |
| 15 | \( y = -\frac{1}{3}x - 1 \) |
| 16 | \( y = -2x - 5 \) |
| 17 | \( y = \frac{1}{2}x + 4 \) |
| Researcher | \( y = -0.25x + 640 \) |

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If you can provide more details about the graphs in Problems 3 and 4 (like slope or points), I can help with those too!

Let me know if you'd like explanations in a different format or need help with graphing!