Check · Mid-year mixed set

1. 1.

   Find the slope of the line through (-2, 0) and (-1, -3).

   Answer. -3

   m = (-3 − 0)/(-1 − -2) = −31 = -3.

2. 2.

   For y = -2x + -5, find y when x = 2.

   Answer. -9

   y = -2(2) + -5 = -9.

3. 3.

   Solve 5x + 6 = 5x + 6.

   Answer. x = 9

   Subtract 5x from both sides, then isolate x. x = 9.

4. 4.

   How many solutions does 3x + 4 = 3x + 7 have?

   Answer. none

   Subtract 3x: 4 = 7, which is never true.

5. 5.

   The graphs of y = x + 3 and y = 2x + 0 intersect at one point. That point is the solution of the system. Check whether (3, 6) lies on y = x + 3. Write a complete answer — Owen will compare with a partner.

   Answer. 3 + 3 = 6 (yes)

   Substitute x = 3: 3 + 3 = 6.

6. 6.

   Solve the system:
   3x + 1y = 23
   3x + 3y = 27 Write a complete answer — Priya will compare with a partner.

   Answer. x = 7, y = 2

   Constructed so (7, 2) satisfies both equations.

7. 7.

   Adult tickets cost $8 and child tickets cost $6. 6 tickets cost $42. If 3 were adult tickets, how many were child tickets? Then Grace needs 2 of that amount. What is the total they need?

   Answer. 6

   3 adults + 3 children = 6 tickets, and 3(8) + 3(6) = 42. Then multiply by 2: 6.

8. 8.

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

   Answer. 1

   m = (4 − 2)/(3 − -1) = 24 = 12. Then multiply by 2: 1.

9. 9.

   A line has slope 2 and y-intercept 6. Write its equation. Write a complete answer — Owen will compare with a partner.

   Answer. y = 2x + 6

   y = mx + b → y = 2x + 6.

10. 10.

    Solve 5x + 8 = 1x + 44. Write a complete answer — Nora will compare with a partner.

    Answer. x = 9

    Subtract 1x from both sides, then isolate x. x = 9.

11. 11.

    Think

    Jonah tried this problem:
    How many solutions does 3x + 2 = 3(x) + 2 have?
    Jonah wrote infinitely many (check this). That is not correct. What is the right answer?

    Answer. infinitely many

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

12. 12.

    Think

    Nora tried this problem:
    The graphs of y = x + 1 and y = 2x + -4 intersect at one point. That point is the solution of the system. Check whether (5, 6) lies on y = x + 1.
    Nora wrote 10 + 1 = 6 (yes). That is not correct. What is the right answer?

    Answer. 5 + 1 = 6 (yes)

    Nora’s answer 10 + 1 = 6 (yes) is off. Substitute x = 5: 5 + 1 = 6.

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