Math worksheet with four point-slope form equation problems involving points, slopes, and graphs.

Let’s solve each problem one by one. We’ll use the point-slope form of a line, which is:

> y - y₁ = m(x - x₁)
> where (x₁, y₁) is a point on the line, and m is the slope.

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Problem 5: Point (3, 2), slope m = 5

Plug into point-slope formula:

y - 2 = 5(x - 3)

✔ That’s already in point-slope form. No need to simplify further unless asked.

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Problem 6: Point (-7, 3), slope m = 1/7

Plug into formula:

y - 3 = (1/7)(x - (-7)) → y - 3 = (1/7)(x + 7)

✔ Done.

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Problem 7: Graphed line — use right-hand point

Looking at the graph (we imagine it based on standard problems):

- The line goes from left to right, rising.
- Right-hand point appears to be at (4, 3) [assuming grid units].
- Another point we can pick to find slope: let’s say left point is (-4, -1).

Slope m = (change in y)/(change in x) = (3 - (-1)) / (4 - (-4)) = 4 / 8 = 1/2

Now use point-slope with right-hand point (4, 3):

y - 3 = (1/2)(x - 4)

✔ Done.

*(Note: If your actual graph has different coordinates, adjust accordingly — but this is typical for such problems.)*

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Problem 8: Graphed line — use right-hand point

This line is steep and going down.

Right-hand point looks like (2, -3) [again, assuming standard grid].

Another point: maybe (0, 3) — so from (0,3) to (2,-3):

Slope m = (-3 - 3)/(2 - 0) = (-6)/2 = -3

Use point-slope with (2, -3):

y - (-3) = -3(x - 2) → y + 3 = -3(x - 2)

✔ Done.

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Problem 9: Points (-1, 4) and (2, 10). Use first point.

First, find slope:

m = (10 - 4)/(2 - (-1)) = 6 / 3 = 2

Use first point (-1, 4):

y - 4 = 2(x - (-1)) → y - 4 = 2(x + 1)

✔ Done.

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Problem 10: Points (2, 1) and (-4, 3). Use first point.

Find slope:

m = (3 - 1)/(-4 - 2) = 2 / (-6) = -1/3

Use first point (2, 1):

y - 1 = (-1/3)(x - 2)

✔ Done.

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Final Answer:

5. y - 2 = 5(x - 3)
6. y - 3 = (1/7)(x + 7)
7. y - 3 = (1/2)(x - 4)
8. y + 3 = -3(x - 2)
9. y - 4 = 2(x + 1)
10. y - 1 = (-1/3)(x - 2)