Point Slope Form Practice Worksheet for Algebra 1 by Lisa Davenport - Free Printable

It looks like you've uploaded a worksheet titled "Graphing + Writing Linear Equations in Point-Slope Form", which contains four problems asking you to:

1. Graph a linear equation given in point-slope form.
2. Identify the point and slope from the equation.
3. Plot the point and use the slope to draw the line.

Let’s go through each problem step by step, explaining how to solve them.

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🔹 Problem 1: Graph \( y - 2 = \frac{1}{2}(x - 3) \)

#### Step 1: Identify the point and slope
The point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
Comparing:
- \( y_1 = 2 \)
- \( x_1 = 3 \)
- So the point is \( (3, 2) \)
- The slope \( m = \frac{1}{2} \)

✔ Point: \( (3, 2) \)
✔ Slope: \( \frac{1}{2} \)

#### Step 2: Graph
1. Plot the point \( (3, 2) \) on the grid.
2. Use the slope \( \frac{1}{2} \): rise 1, run 2.
- From \( (3, 2) \), go up 1 unit, right 2 units → new point: \( (5, 3) \)
- Or down 1, left 2 → \( (1, 1) \)
3. Draw a straight line through these points.

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🔹 Problem 2: Graph \( y - 5 = 4(x + 2) \)

First, rewrite it as:
\[
y - 5 = 4(x - (-2))
\]

So:
- \( y_1 = 5 \)
- \( x_1 = -2 \)
- Point: \( (-2, 5) \)
- Slope: \( m = 4 \) (which is \( \frac{4}{1} \))

✔ Point: \( (-2, 5) \)
✔ Slope: \( 4 \)

#### Step 2: Graph
1. Plot \( (-2, 5) \)
2. Slope = 4 → rise 4, run 1
- From \( (-2, 5) \), go up 4, right 1 → \( (-1, 9) \)
- Or down 4, left 1 → \( (-3, 1) \)
3. Draw the line.

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🔹 Problem 3: Graph \( y + 4 = 2(x - 3) \)

Rewrite:
\[
y - (-4) = 2(x - 3)
\]

So:
- \( y_1 = -4 \)
- \( x_1 = 3 \)
- Point: \( (3, -4) \)
- Slope: \( m = 2 \) → rise 2, run 1

✔ Point: \( (3, -4) \)
✔ Slope: \( 2 \)

#### Step 2: Graph
1. Plot \( (3, -4) \)
2. From there, go up 2, right 1 → \( (4, -2) \)
3. Draw the line.

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🔹 Problem 4: Graph \( y - 1 = \frac{2}{3}(x + 6) \)

Rewrite:
\[
y - 1 = \frac{2}{3}(x - (-6))
\]

So:
- \( y_1 = 1 \)
- \( x_1 = -6 \)
- Point: \( (-6, 1) \)
- Slope: \( \frac{2}{3} \) → rise 2, run 3

✔ Point: \( (-6, 1) \)
✔ Slope: \( \frac{2}{3} \)

#### Step 2: Graph
1. Plot \( (-6, 1) \)
2. From there, go up 2, right 3 → \( (-3, 3) \)
3. Or down 2, left 3 → \( (-9, -1) \)
4. Draw the line.

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✔ Summary of Answers:

| Problem | Point | Slope |
|--------|-------------|-----------|
| 1 | (3, 2) | \( \frac{1}{2} \) |
| 2 | (-2, 5) | 4 |
| 3 | (3, -4) | 2 |
| 4 | (-6, 1) | \( \frac{2}{3} \) |

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📝 How to Fill Out the Worksheet:

For each problem:
1. Write the point in the "Point:" box.
2. Write the slope in the "Slope:" box.
3. On the graph:
- Plot the point.
- Use the slope to find another point.
- Draw a straight line through both points.

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