Unit 5: Linear Functions and Solving Equations

Multiple Choice

1. Which of the following equations will have no solution when simplified?

• A. 3𝑥 – 4 = 5𝑥 + 2

• B. 8𝑥 + 5 = 8𝑥

• C. 5𝑥 = 5𝑥

• D. 4𝑥 = 32

Multiple Choice

2. Find the value of x: 𝟒𝒙 + 𝟐(𝒙 – 𝟑) = 𝟔𝒙 – 𝟔

• A. 𝑥 = 0

• B. 𝑥 = 6

• C. Infinite solutions

• D. No solution

Multiple Choice

3. Simplify the expression: $$\frac{1}{2}(𝟒𝒙+𝟔)=−𝟓𝒙+𝟐𝟒.𝟕$$

• A. 𝑥 = 3.1

• B. 𝑥 = 3

• C. 𝑥 = 7

• D. 𝑥 = −7.23

Multiple Choice

4. A student worked the equation on the left, showing his steps. In which step did he make a mistake?

• A. Step 1

• B. Step 2

• C. Step 3

• D. He made no error.

Multiple Choice

5. Find the value of x: $$\frac{x}{2}+𝟓=𝟏𝟐$$

• A. 𝑥 = 14

• B. 𝑥 = 7

• C. 𝑥 = 34

• D. No solution

Multiple Choice

6. Solve the equation for x: $$\frac{3}{4}+\frac{1}{2}x=x-\frac{1}{4}$$

• A. 𝑥 = $$\frac{1}{2}$$

• B. 𝑥 = 5

• C. 𝑥 = 1

• D. 𝑥 = 2

Multiple Choice

7. Solve the equation for x:

$$−𝟏𝟎(𝒙+𝟐)−𝟓𝒙=−𝟗𝒙+𝟏𝟔$$

• A. 𝑥 = −6

• B. 𝑥 = 6

• C. 𝑥= $$\frac{1}{6}$$

• D. 𝑥= $$\frac{3}{2}$$

Multiple Choice

8. James is remodeling his home and wants to put in all hard-wood flooring. The graph on the left shows the price of hard-wood flooring per square foot. What is the unit rate per square foot of hard-wood flooring?

• A. $500 per square foot of flooring

• B. $6.25 per square foot of flooring

• C. $100 per square foot of flooring

• D. $5 per square foot of flooring

Multiple Choice

9. Mike and Anna are having a weight loss competition. Mike wants to practice kickboxing to burn calories while Anna prefers to run. Mike records his calories burned in the table and Anna graphs her calories burned in the graph.

Who burns more calories per hour?

• A. Mike and Anna burn the same amount of calories per minute

• B. Mike burns more calories per minute than Anna.

• C. Anna burns more calories per minute than Mike.

• D. There is not enough information to determine who burns more calories per minute.

Multiple Choice

10. Payton and Elizabeth are working on their keyboarding skills. Payton uses the equation below to show how many words (W) she can type per minute (m). The graph below represents how many words per minute Elizabeth can type.

Which statement below is most accurate?

• A. Payton types at a faster rate.

• B. Elizabeth types at a faster rate.

• C. Payton and Elizabeth type at the same rate.

• D. There is not enough information to compare the typing rates of Payton and Elizabeth.

Multiple Choice

14. Kinnady is applying to work at two different restaurants to earn money while she attends college. Both restaurants offer an hourly rate of pay as well as any tips she earns during her shift. The first restaurant gave their pay scale information in a table, while the second restaurant gave their information in a graph. Both are shown on the left.

Which restaurant will pay Kinnady more money per hour?

• A. Restaurant 1 will pay more per hour.

• B. Restaurant 2 will pay more per hour.

• C. Both restaurants will pay the same amount per hour.

• D. There is not enough information provided to compare pay rates.

Multiple Choice

15. Triangle 𝐴𝐵𝐶 is similar to triangle 𝑋𝑌𝐶, and the hypotenuses of the triangles both lie on line $$\overline{AX}$$ . The slope between point C and point A is 23. What is the slope between point X and point C?

• A. $$-\frac{2}{3}$$

• B. $$-\frac{3}{2}$$

• C. $$\frac{2}{3}$$

• D. $$\frac{3}{2}$$

Multiple Choice

16. Triangle 𝐴𝐵𝐶 is similar to triangle 𝑋𝑌𝐶, and the hypotenuses of the triangles both lie on line $$\overline{AX}$$ .

Which proportional statement below is TRUE?

Multiple Choice

17. Consider the graph shown. Which statement is true about Line 1 and Line 2?

• A. Line 1: 𝑦=𝑚𝑥+𝑏 Line 2: 𝑦=𝑚𝑥

• B. Line 1: 𝑦=𝑚𝑥 Line 2: 𝑦=𝑚𝑥+𝑏

• C. Line 1: 𝑦=𝑚𝑥+𝑏 Line 2: 𝑦=𝑚𝑥−𝑏

• D. Line 1: 𝑦=𝑚𝑥 Line 2: 𝑦=𝑚𝑥−𝑏

Multiple Choice

18. Given the equation $$𝒚=\frac{2}{3}𝒙+𝟒$$ , which statement below is FALSE?

• A. The line of the equation will have a positive slope, going up from left to right.

• B. The y-intercept of the line will be (0, 4).

• C. The line of the equation will have a negative slope, going down from left to right.

• D. The graph will be a line with a constant slope which rises 2 units for every 3 units across.

Multiple Choice

19. Given the equation $$𝒚=−𝟒𝒙$$ , which statement below is TRUE?

• A. The line of the equation will go down and through the origin.

• B. The line of the equation will go up and through the origin.

• C. The line of the equation will go down and through the point (0, -4)

• D. The line of the equation will go up and through the point (0, -4)