Worksheet for practicing writing linear equations from a point and slope.

I will solve the problem presented in the image, which is to write an equation of a line that passes through a given point and has a specified slope. I will go through each problem one by one.

The general formula for the equation of a line in point-slope form is:
`y - y₁ = m(x - x₁)`
where `(x₁, y₁)` is a point on the line and `m` is the slope.

Let's start with problem 1.

Problem 1: (3, 0) slope of 3

- Point: (x₁, y₁) = (3, 0)
- Slope: m = 3

Using the point-slope formula:
`y - 0 = 3(x - 3)`
`y = 3x - 9`

This matches the provided answer: `y = 3x - 9`.

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Problem 2: (2, 4) slope of 2

- Point: (x₁, y₁) = (2, 4)
- Slope: m = 2

Using the point-slope formula:
`y - 4 = 2(x - 2)`
`y - 4 = 2x - 4`
`y = 2x`

This matches the provided answer: `y = 2x`.

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Problem 3: (5, 3) slope of -1

- Point: (x₁, y₁) = (5, 3)
- Slope: m = -1

Using the point-slope formula:
`y - 3 = -1(x - 5)`
`y - 3 = -x + 5`
`y = -x + 8`

This matches the provided answer: `y = -x + 8`.

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Problem 4: (-4, 6) slope of -2

- Point: (x₁, y₁) = (-4, 6)
- Slope: m = -2

Using the point-slope formula:
`y - 6 = -2(x - (-4))`
`y - 6 = -2(x + 4)`
`y - 6 = -2x - 8`
`y = -2x - 2`

This matches the provided answer: `y = -2x - 2`.

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Problem 5: (1, -2) slope of 1/2

- Point: (x₁, y₁) = (1, -2)
- Slope: m = 1/2

Using the point-slope formula:
`y - (-2) = (1/2)(x - 1)`
`y + 2 = (1/2)x - 1/2`
`y = (1/2)x - 1/2 - 2`
`y = (1/2)x - 5/2`

This matches the provided answer: `y = (1/2)x - 5/2`.

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Problem 6: (-1, -3) slope of 4

- Point: (x₁, y₁) = (-1, -3)
- Slope: m = 4

Using the point-slope formula:
`y - (-3) = 4(x - (-1))`
`y + 3 = 4(x + 1)`
`y + 3 = 4x + 4`
`y = 4x + 1`

This matches the provided answer: `y = 4x + 1`.

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Problem 7: (2, 6) slope of 2

- Point: (x₁, y₁) = (2, 6)
- Slope: m = 2

Using the point-slope formula:
`y - 6 = 2(x - 2)`
`y - 6 = 2x - 4`
`y = 2x + 2`

This matches the provided answer: `y = 2x + 2`.

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Problem 8: (-1, 4) slope of 3

- Point: (x₁, y₁) = (-1, 4)
- Slope: m = 3

Using the point-slope formula:
`y - 4 = 3(x - (-1))`
`y - 4 = 3(x + 1)`
`y - 4 = 3x + 3`
`y = 3x + 7`

This matches the provided answer: `y = 3x + 7`.

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Problem 9: (-1, -2) slope of 1/2

- Point: (x₁, y₁) = (-1, -2)
- Slope: m = 1/2

Using the point-slope formula:
`y - (-2) = (1/2)(x - (-1))`
`y + 2 = (1/2)(x + 1)`
`y + 2 = (1/2)x + 1/2`
`y = (1/2)x + 1/2 - 2`
`y = (1/2)x - 3/2`

This matches the provided answer: `y = (1/2)x - 3/2`.

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All the equations provided in the image are correct. The solution process involves using the point-slope form of a linear equation, substituting the given point and slope, and then simplifying to get the equation in slope-intercept form (`y = mx + b`).