L8 · Proportional relationships and slope

1. 1.

   Find the slope of the line through (3, 2) and (8, 4).

   Answer. 25

   m = (4 − 2)/(8 − 3) = 25 = 25.

2. 2.

   Find the slope of the line through (-3, -2) and (-1, -1).

   Answer. 12

   m = (-1 − -2)/(-1 − -3) = 12 = 12.

3. 3.

   Find the slope of the line through (-3, -1) and (2, -2).

   Answer. −15

   m = (-2 − -1)/(2 − -3) = −15 = −15.

4. 4.

   Find the slope of the line through (-1, 0) and (0, -1).

   Answer. -1

   m = (-1 − 0)/(0 − -1) = −11 = -1.

5. 5.

   Find the slope of the line through (2, 0) and (6, 2). Then Jonah needs 2 of that amount. What is the total they need?

   Answer. 1

   m = (2 − 0)/(6 − 2) = 24 = 12. Then multiply by 2: 1.

6. 6.

   Find the slope of the line through (2, -4) and (5, -2). Then Malik needs 4 of that amount. What is the total they need?

   Answer. 223

   m = (-2 − -4)/(5 − 2) = 23 = 23. Then multiply by 4: 223.

7. 7.

   Find the slope of the line through (-1, 4) and (1, 2). Then Elena needs 3 of that amount. What is the total they need?

   Answer. -3

   m = (2 − 4)/(1 − -1) = −22 = -1. Then multiply by 3: -3.

8. 8.

   Find the slope of the line through (0, 0) and (2, -2). Then Nora needs 5 of that amount. What is the total they need?

   Answer. -5

   m = (-2 − 0)/(2 − 0) = −22 = -1. Then multiply by 5: -5.

9. 9.

   Find the slope of the line through (1, 1) and (4, -2). Then Owen needs 3 of that amount. What is the total they need?

   Answer. -3

   m = (-2 − 1)/(4 − 1) = −33 = -1. Then multiply by 3: -3.

10. 10.

    Find the slope of the line through (2, -1) and (3, -5). Then Grace needs 3 of that amount. What is the total they need?

    Answer. -12

    m = (-5 − -1)/(3 − 2) = −41 = -4. Then multiply by 3: -12.

11. 11.

    Think

    Jonah tried this problem:
    Find the slope of the line through (3, 1) and (8, 3).
    Jonah wrote 26. That is not correct. What is the right answer?

    Answer. 25

    Jonah’s answer 26 is off. m = (3 − 1)/(8 − 3) = 25 = 25.

12. 12.

    Think

    Ava tried this problem:
    Find the slope of the line through (-1, -1) and (0, 3).
    Ava wrote 8. That is not correct. What is the right answer?

    Answer. 4

    Ava’s answer 8 is off. m = (3 − -1)/(0 − -1) = 41 = 4.

Original extra practice. Keys are computed from the items, not guessed.