UA · Unit 3 review

1. 1.

   Find the slope of the line through (3, 1) and (4, 6).

   Answer. 5

   m = (6 − 1)/(4 − 3) = 51 = 5.

2. 2.

   A line has slope 3 and y-intercept -4. Write its equation.

   Answer. y = 3x - 4

   y = mx + b → y = 3x + -4.

3. 3.

   Solve 3x + 5 = 5x − 1.

   Answer. x = 3

   Subtract 5x from both sides, then isolate x. x = 3.

4. 4.

   How many solutions does 3x + 6 = 3x + 9 have?

   Answer. none

   Subtract 3x: 6 = 9, 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 — Elena will compare with a partner.

   Answer. 3 + 1 = 4 (yes)

   Substitute x = 3: 3 + 1 = 4.

6. 6.

   Solve the system:
   4x + 1y = 18
   2x + 1y = 10 Write a complete answer — Ava will compare with a partner.

   Answer. x = 4, y = 2

   Constructed so (4, 2) satisfies both equations.

7. 7.

   Adult tickets cost $10 and child tickets cost $7. 7 tickets cost $58. If 3 were adult tickets, how many were child tickets? Then Luis needs 5 of that amount. What is the total they need?

   Answer. 20

   3 adults + 4 children = 7 tickets, and 3(10) + 4(7) = 58. Then multiply by 5: 20.

8. 8.

   Find the slope of the line through (0, -2) and (3, -6). Then Grace needs 4 of that amount. What is the total they need?

   Answer. −513

   m = (-6 − -2)/(3 − 0) = −43 = −113. Then multiply by 4: −513.

9. 9.

   For y = -3x + 4, find y when x = 2. Then Priya needs 2 of that amount. What is the total they need?

   Answer. -4

   y = -3(2) + 4 = -2. Then multiply by 2: -4.

10. 10.

    Solve 4x + 3 = 1x + 12. Write a complete answer — Grace will compare with a partner.

    Answer. x = 3

    Subtract 1x from both sides, then isolate x. x = 3.

11. 11.

    Think

    Owen tried this problem:
    How many solutions does 3x + 7 = 3(x) + 7 have?
    Owen wrote infinitely many (check this). That is not correct. What is the right answer?

    Answer. infinitely many

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

12. 12.

    Think

    Luis tried this problem:
    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.
    Luis wrote 6 + 1 = 4 (yes). That is not correct. What is the right answer?

    Answer. 3 + 1 = 4 (yes)

    Luis’s answer 6 + 1 = 4 (yes) is off. Substitute x = 3: 3 + 1 = 4.

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