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

I'll solve this worksheet on graphing and writing linear equations in point-slope form. Let me work through each problem step by step.

Problem 1: Graph y - 2 = 3/5(x - 3)

First, I need to identify the point and slope from the point-slope form equation.
The general point-slope form is: y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line and m is the slope.

For this equation:
- Point: (3, 2) [from (x - 3) and (y - 2)]
- Slope: 3/5

To graph this, I would:
1. Plot the point (3, 2) on the coordinate plane
2. Use the slope 3/5 (rise/run) to find another point: go up 3 units and right 5 units from (3, 2) to get to (8, 5)
3. Draw a line through these points

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

Rewriting this in standard point-slope form: y - (-5) = -4(x - (-2))

For this equation:
- Point: (-2, -5) [from (x + 2) which is (x - (-2)) and (y + 5) which is (y - (-5))]
- Slope: -4 (which can be written as -4/1)

To graph this, I would:
1. Plot the point (-2, -5) on the coordinate plane
2. Use the slope -4/1 (rise/run) to find another point: go down 4 units and right 1 unit from (-2, -5) to get to (-1, -9)
3. Draw a line through these points

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

For this equation:
- Point: (3, 4) [from (x - 3) and (y - 4)]
- Slope: 2 (which can be written as 2/1)

To graph this, I would:
1. Plot the point (3, 4) on the coordinate plane
2. Use the slope 2/1 (rise/run) to find another point: go up 2 units and right 1 unit from (3, 4) to get to (4, 6)
3. Draw a line through these points

Problem 4: Graph y - 1 = 1/2(x + 6)

Rewriting this in standard point-slope form: y - 1 = 1/2(x - (-6))

For this equation:
- Point: (-6, 1) [from (x + 6) which is (x - (-6)) and (y - 1)]
- Slope: 1/2

To graph this, I would:
1. Plot the point (-6, 1) on the coordinate plane
2. Use the slope 1/2 (rise/run) to find another point: go up 1 unit and right 2 units from (-6, 1) to get to (-4, 2)
3. Draw a line through these points

Now I'll fill in the answers for each problem:

Problem 1:
- Point: (3, 2)
- Slope: 3/5

Problem 2:
- Point: (-2, -5)
- Slope: -4

Problem 3:
- Point: (3, 4)
- Slope: 2

Problem 4:
- Point: (-6, 1)
- Slope: 1/2