Name_______________________________ Date______________ Period_______

Study Guide – 9 Weeks Test

Solve each equation. Show all work.

1) 𝟏

𝟔(𝒙 − 𝟒) =

𝟐

𝟑𝒙 +

𝟒

𝟑 2) −𝟓(𝒙 − 𝟒) = 𝟏𝟎𝒙 + 𝟏𝟎

3) −𝟑𝒚 + 𝟏 = 𝒚 + 𝟗 − 𝟒𝒚 4) 𝟖 − 𝟕(𝟒𝒙 − 𝟐) = −𝟐𝟖𝒙 + 𝟐𝟐

5) 𝟏. 𝟓𝒎 − 𝟏 = −𝟓 + 𝟏. 𝟕𝒎 6) 𝟐(𝒚 − 𝟒) + 𝟖 =𝟏

𝟐(𝟔𝒚 + 𝟐𝟎)

8th Grade

7) Determine if each equation has no solution, one solution, or infinite many solutions. 𝟑(𝒙 + 𝟕) = 𝟐(𝒙 + 𝟕) + 𝒙 𝟑(𝒙 + 𝟕) = 𝟒𝒙 − 𝒙 + 𝟐𝟏 𝟑𝒙 + 𝟕 = 𝟓𝒙 + 𝟕 − 𝟑𝒙 8) The equation below has infinite many solutions. 𝒂𝒙 + 𝒃 = 𝟒(𝟐𝒙 + 𝟑) − 𝟏𝟎𝒙 For this to be true, what must be the value of a? What must be the value of b? Solve and graph each inequality. Show all work.

9) −𝟐𝒚 − 𝟑 ≤ −𝟓 10) 𝟔 − 𝒙 > 𝟑

11) 𝟑(𝒙 − 𝟒) ≥ −𝟓𝒙 + 𝟒

12) CIRCLE the numbers that could be solutions to the inequality listed.

𝒙 < 𝟓

𝒙 > −𝟐

𝒙 ≥ 𝟗

𝒙 ≤ −𝟕𝟎 13) Complete the input/output table using the given function rule. 𝒚 = 𝟑𝒙 – 𝟐

14) Label each with either a Function or Not a Function.

-15 0 5 6 18

-4 -2 -1 8 30

-9 8.9 9 10 21

-80 -70 -50 -1 10

x -2 -1 4 0 7 5

y

15) Which table creates the graph shown. 16) Create a model for the equation 𝒚 = 𝟐𝒙 − 𝟑 by making a table of order pairs and graphing.

What is the y-intercept? What is the slope? 17)

X Y

18) Write an equation that represents the table. 19) Name the slope and y-intercept for each equation or table below.

SLOPE Y-Intercept 𝒚 = 𝟐𝒙 𝒚 = 𝟒𝒙 − 𝟓 𝒚 = 𝟑 − 𝟔𝒙

20) What other word means SLOPE? What other word means Y-Intercept? A. x-intercept A. x-intercept C. initial value B. initial value B. rate of change C. rate of change

21) 22) Label each as either linear or nonlinear.

𝒚 = 𝒙𝟐 − 𝟓 𝒚 = 𝒙 − 𝟒 𝒚 = 𝟐𝒙 + 𝟏 23) Sunset Splash and Spa charges their customers a fee for entering plus an amount per hour of stay.

What is the initial fee for entering the Spa?

What is the rate of change?

What would a person be charged for spending 𝟖 hours at the spa?

Time (hours)

Cost $

2 41

6 73 10 105

24) 25) Randy is shopping for CD’s to give as gifts to his friends. He is considering two stores. The pricing for each store is shown below.

CD Express Music Place 𝟔 CD’s for $𝟕𝟓

Which store is cheaper per CD?

How much will Randy save per CD at this store?

Number of CD’s

Cost $

3 45 5 75

8 120 10 150

26) State if each represents a proportional or non-proportional relationship.

Every 3 out of 12 people

live in a rural area. The City Pool costs $8 per

day to visit during the

summer. There is also a $25

yearly registration fee.

ANSWER KEY

Name_______________________________ Date______________ Period_______

Study Guide – 9 Weeks Test

Solve each equation. Show all work.

1) 𝟏

𝟔(𝒙 − 𝟒) =

𝟐

𝟑𝒙 +

𝟒

𝟑 2) −𝟓(𝒙 − 𝟒) = 𝟏𝟎𝒙 + 𝟏𝟎

Answer: −𝟒 Answer: 𝟐

𝟑

3) −𝟑𝒚 + 𝟏 = 𝒚 + 𝟗 − 𝟒𝒚 4) 𝟖 − 𝟕(𝟒𝒙 − 𝟐) = −𝟐𝟖𝒙 + 𝟐𝟐 Answer: No solution Answer: Infinite Many Solutions

5) 𝟏. 𝟓𝒎 − 𝟏 = −𝟓 + 𝟏. 𝟕𝒎 6) 𝟐(𝒚 − 𝟒) + 𝟖 =𝟏

𝟐(𝟔𝒚 + 𝟐𝟎)

Answer: 20 Answer: -10

Answer Key

8th Grade

7) Determine if each equation has no solution, one solution, or infinite many solutions. 𝟑(𝒙 + 𝟕) = 𝟐(𝒙 + 𝟕) + 𝒙 Answer: no solution 𝟑(𝒙 + 𝟕) = 𝟒𝒙 − 𝒙 + 𝟐𝟏 Answer: Infinite Many Solutions 𝟑𝒙 + 𝟕 = 𝟓𝒙 + 𝟕 − 𝟑𝒙 Answer: 1 solution 8) The equation below has infinite many solutions. 𝒂𝒙 + 𝒃 = 𝟒(𝟐𝒙 + 𝟑) − 𝟏𝟎𝒙 For this to be true, what must be the value of a? What must be the value of b? a must be -2 b must be 12 Solve and graph each inequality. Show all work.

9) −𝟐𝒚 − 𝟑 ≤ −𝟓 Symbol Flip! 𝒚 ≥ 𝟏 10) 𝟔 − 𝒙 > 𝟑 Symbol Flip! 𝒙 < 𝟑

11) 𝟑(𝒙 − 𝟒) ≥ −𝟓𝒙 + 𝟒 𝒙 ≥ 𝟐

12) CIRCLE the numbers that could be solutions to the inequality listed.

𝒙 < 𝟓

𝒙 > −𝟐

𝒙 ≥ 𝟗

𝒙 ≤ −𝟕𝟎 13) Complete the input/output table using the given function rule. 𝒚 = 𝟑𝒙 – 𝟐

14) Label each with either a Function or Not a Function. Function Not a Function

-15 0 5 6 18

-4 -2 -1 8 30

-9 8.9 9 10 21

-80 -70 -50 -1 10

x -2 -1 4 0 7 5

y -8 -5 10 -2 19 13

15) Which table creates the graph shown. 16) Create a model for the equation 𝒚 = 𝟐𝒙 − 𝟑 by making a table of order pairs and graphing.

What is the y-intercept? -3 What is the slope? 2 17)

X Y

-1 -5

0 -3

1 -1

2 1

3 3

18) Write an equation that represents the table. 𝒚 = 𝒙 – 𝟓 19) Name the slope and y-intercept for each equation or table below.

SLOPE Y-Intercept

𝒚 = 𝟐𝒙 2 0

𝒚 = 𝟒𝒙 − 𝟓 4 -5 𝒚 = 𝟑 − 𝟔𝒙 -6 3

-1 3

3 6 20) What other word means SLOPE? What other word means Y-Intercept? A. x-intercept A. x-intercept C. initial value B. initial value B. rate of change C. rate of change

21) $200 22) Label each as either linear or nonlinear.

𝒚 = 𝒙𝟐 − 𝟓 𝒚 = 𝒙 − 𝟒 𝒚 = 𝟐𝒙 + 𝟏 nonlinear linear linear nonlinear 23) Sunset Splash and Spa charges their customers a fee for entering plus an amount per hour of stay.

What is the initial fee for entering the Spa? Answer: $25

What is the rate of change? Answer: $8

What would a person be charged for spending 𝟖 hours at the spa? Answer: $89

Time (hours)

Cost $

2 41

6 73 10 105

24) 25) Randy is shopping for CD’s to give as gifts to his friends. He is considering two stores. The pricing for each store is shown below.

CD Express Music Place 𝟔 CD’s for $𝟕𝟓

Which store is cheaper per CD? Answer: Music Place

How much will Randy save per CD at this store? Answer: $15 – $12.50 = $2.50

Number of CD’s

Cost $

3 45

5 75 8 120

10 150

26) State if each represents a proportional or non-proportional relationship. Non-proportional Proportional Proportional Non-Proportional Non-Proportional Proportional

Every 3 out of 12 people

live in a rural area. The City Pool costs $8 per

day to visit during the

summer. There is also a $25

yearly registration fee.