Solved Finding Slope From A Table Practice Write the | Chegg.com - Free Printable

Explanation:
We are given tables of (x, y) values and need to find the slope $ m = \frac{\Delta y}{\Delta x} $ for each.
Recall:
- $ \Delta y = y_2 - y_1 $
- $ \Delta x = x_2 - x_1 $
- Slope $ m = \frac{y_2 - y_1}{x_2 - x_1} $ — it should be the same no matter which two points we pick (if the points lie on a straight line, which they do here).

Let’s compute each one carefully.

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Problem 1:
Points: (-3, 1), (0, 4), (-5, -1), (-2, 2), (6, 10)
Pick first two:
$ \Delta y = 4 - 1 = 3 $
$ \Delta x = 0 - (-3) = 3 $
$ m = \frac{3}{3} = 1 $
Check with another pair: (-2, 2) and (6, 10):
$ \Delta y = 10 - 2 = 8 $, $ \Delta x = 6 - (-2) = 8 $ → $ m = 1 $. ✔️
So:
$ \Delta y = 3 $, $ \Delta x = 3 $, $ m = 1 $

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Problem 2:
Points: (-6, 27), (2, 3), (4, -3), (-8, 33), (9, -18)
Use (-6, 27) and (2, 3):
$ \Delta y = 3 - 27 = -24 $
$ \Delta x = 2 - (-6) = 8 $
$ m = \frac{-24}{8} = -3 $
Check with (4, -3) and (9, -18):
$ \Delta y = -18 - (-3) = -15 $, $ \Delta x = 9 - 4 = 5 $ → $ -15/5 = -3 $. ✔️
So:
$ \Delta y = -24 $, $ \Delta x = 8 $, $ m = -3 $

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Problem 3:
Points: (5, 27), (0, -8), (9, 55), (-4, -36), (4, 20)
Use (0, -8) and (5, 27):
$ \Delta y = 27 - (-8) = 35 $
$ \Delta x = 5 - 0 = 5 $
$ m = 35/5 = 7 $
Check with (4, 20) and (0, -8):
$ \Delta y = 20 - (-8) = 28 $, $ \Delta x = 4 - 0 = 4 $ → $ 28/4 = 7 $. ✔️
So:
$ \Delta y = 35 $, $ \Delta x = 5 $, $ m = 7 $

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Problem 4:
Points: (1, 0), (-7, -24), (-5, -18), (7, 18), (-9, -30)
Use (1, 0) and (7, 18):
$ \Delta y = 18 - 0 = 18 $
$ \Delta x = 7 - 1 = 6 $
$ m = 18/6 = 3 $
Check with (-7, -24) and (-5, -18):
$ \Delta y = -18 - (-24) = 6 $, $ \Delta x = -5 - (-7) = 2 $ → $ 6/2 = 3 $. ✔️
So:
$ \Delta y = 18 $, $ \Delta x = 6 $, $ m = 3 $

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Problem 5:
Points: (-3, 20), (-5, 32), (-4, 26), (-2, 14), (8, -46)
Use (-3, 20) and (-5, 32):
$ \Delta y = 32 - 20 = 12 $
$ \Delta x = -5 - (-3) = -2 $
$ m = 12 / (-2) = -6 $
Check with (-2, 14) and (8, -46):
$ \Delta y = -46 - 14 = -60 $, $ \Delta x = 8 - (-2) = 10 $ → $ -60/10 = -6 $. ✔️
So:
$ \Delta y = 12 $, $ \Delta x = -2 $, $ m = -6 $

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Problem 6:
Points: (5, -4), (0, -9), (-7, -16), (-5, -14), (-3, -12)
Use (0, -9) and (5, -4):
$ \Delta y = -4 - (-9) = 5 $
$ \Delta x = 5 - 0 = 5 $
$ m = 5/5 = 1 $
Check with (-5, -14) and (-3, -12):
$ \Delta y = -12 - (-14) = 2 $, $ \Delta x = -3 - (-5) = 2 $ → $ 2/2 = 1 $. ✔️
So:
$ \Delta y = 5 $, $ \Delta x = 5 $, $ m = 1 $

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Problem 7:
Points: (-6, -2), (-1, -4.5), (4, -7), (-7, -1.5), (7, -8.5)
Use (-6, -2) and (4, -7):
$ \Delta y = -7 - (-2) = -5 $
$ \Delta x = 4 - (-6) = 10 $
$ m = -5/10 = -0.5 $
Check with (-1, -4.5) and (7, -8.5):
$ \Delta y = -8.5 - (-4.5) = -4 $, $ \Delta x = 7 - (-1) = 8 $ → $ -4/8 = -0.5 $. ✔️
So:
$ \Delta y = -5 $, $ \Delta x = 10 $, $ m = -0.5 $

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Problem 8:
Points: (-7, -2), (6, 11), (-5, 0), (9, 14), (-3, 2)
Use (-7, -2) and (6, 11):
$ \Delta y = 11 - (-2) = 13 $
$ \Delta x = 6 - (-7) = 13 $
$ m = 13/13 = 1 $
Check with (-5, 0) and (-3, 2):
$ \Delta y = 2 - 0 = 2 $, $ \Delta x = -3 - (-5) = 2 $ → $ 2/2 = 1 $. ✔️
So:
$ \Delta y = 13 $, $ \Delta x = 13 $, $ m = 1 $

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Problem 9:
Points: (-2, -6.5), (4, -8), (7, -8.75), (-8, -5), (9, -9.25)
Use (-2, -6.5) and (4, -8):
$ \Delta y = -8 - (-6.5) = -1.5 $
$ \Delta x = 4 - (-2) = 6 $
$ m = -1.5 / 6 = -0.25 $
Check with (7, -8.75) and (-8, -5):
$ \Delta y = -5 - (-8.75) = 3.75 $, $ \Delta x = -8 - 7 = -15 $
$ 3.75 / (-15) = -0.25 $. ✔️
So:
$ \Delta y = -1.5 $, $ \Delta x = 6 $, $ m = -0.25 $

Now write all answers in order:

1. Δy = 3, Δx = 3, m = 1
2. Δy = -24, Δx = 8, m = -3
3. Δy = 35, Δx = 5, m = 7
4. Δy = 18, Δx = 6, m = 3
5. Δy = 12, Δx = -2, m = -6
6. Δy = 5, Δx = 5, m = 1
7. Δy = -5, Δx = 10, m = -0.5
8. Δy = 13, Δx = 13, m = 1
9. Δy = -1.5, Δx = 6, m = -0.25

Final Answer:
1. Δy = 3, Δx = 3, m = 1
2. Δy = -24, Δx = 8, m = -3
3. Δy = 35, Δx = 5, m = 7
4. Δy = 18, Δx = 6, m = 3
5. Δy = 12, Δx = -2, m = -6
6. Δy = 5, Δx = 5, m = 1
7. Δy = -5, Δx = 10, m = -0.5
8. Δy = 13, Δx = 13, m = 1
9. Δy = -1.5, Δx = 6, m = -0.25