MIA · Mixed set · Unit 3

1. 1.

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

   Answer. -3

   m = (-2 − 1)/(-2 − -3) = −31 = -3.

2. 2.

   A line has slope 3 and y-intercept 3. Write its equation.

   Answer. y = 3x + 3

   y = mx + b → y = 3x + 3.

3. 3.

   Solve 4x + 3 = 2x + 11.

   Answer. x = 4

   Subtract 2x from both sides, then isolate x. x = 4.

4. 4.

   How many solutions does 2x + 5 = 2x + 8 have?

   Answer. none

   Subtract 2x: 5 = 8, which is never true.

5. 5.

   The graphs of y = x + 1 and y = 2x + -2 intersect at one point. That point is the solution of the system. Check whether (3, 4) lies on y = x + 1. Write a complete answer — Mei will compare with a partner.

   Answer. 3 + 1 = 4 (yes)

   Substitute x = 3: 3 + 1 = 4.

6. 6.

   Solve the system:
   4x + 3y = 10
   1x + 2y = 5 Write a complete answer — Jonah will compare with a partner.

   Answer. x = 1, y = 2

   Constructed so (1, 2) satisfies both equations.

7. 7.

   Adult tickets cost $14 and child tickets cost $6. 8 tickets cost $88. If 5 were adult tickets, how many were child tickets? Then Grace needs 3 of that amount. What is the total they need?

   Answer. 9

   5 adults + 3 children = 8 tickets, and 5(14) + 3(6) = 88. Then multiply by 3: 9.

8. 8.

   Find the slope of the line through (-3, -3) and (2, -4). Then Jonah needs 5 of that amount. What is the total they need?

   Answer. −1

   m = (-4 − -3)/(2 − -3) = −15 = −15. Then multiply by 5: −1.

9. 9.

   For y = -1x + 4, find y when x = 4. Then Luis needs 4 of that amount. What is the total they need?

   Answer. 0

   y = -1(4) + 4 = 0. Then multiply by 4: 0.

10. 10.

    Solve 6x + 8 = 3x + 32. Write a complete answer — Owen will compare with a partner.

    Answer. x = 8

    Subtract 3x from both sides, then isolate x. x = 8.

11. 11.

    Think

    Priya tried this problem:
    How many solutions does 5x + 6 = 5(x) + 6 have?
    Priya wrote infinitely many (check this). That is not correct. What is the right answer?

    Answer. infinitely many

    Priya’s answer infinitely many (check this) is off. Both sides are identical, so every x works.

12. 12.

    Think

    Jonah tried this problem:
    The graphs of y = x + 0 and y = 2x + -3 intersect at one point. That point is the solution of the system. Check whether (3, 3) lies on y = x + 0.
    Jonah wrote 4 + 0 = 3 (yes). That is not correct. What is the right answer?

    Answer. 3 + 0 = 3 (yes)

    Jonah’s answer 4 + 0 = 3 (yes) is off. Substitute x = 3: 3 + 0 = 3.

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