Unit 2 Post Test: Linear Equations and Relationships

What is the equation of the given graph?

• y = -2x - 3

• y = 1/2x + 3

• y = 2x - 3

• y = 1/2x - 3

Answer explanation

The graph has a positive slope and a y-intercept of -3. The equation y = 2x - 3 matches these characteristics, indicating a steep incline, while the other options do not fit the slope or intercept.

Which graph shows a function that is increasing continuously as x increases?

• 
• 
• 
• 

Answer explanation

This graph shows a continuously increasing function as x increases.

A science club launched a model rocket and collected data during the flight. The graph below represents a function of the rocket’s height, based on the time after launch. Which statement best describes the graph of the function?

• The graph is non-linear, and it decreases continuously for times less than 3 seconds and increases continuously for times greater than 3 seconds.

• The graph is non-linear, and it increases continuously for times less than 3 seconds and decreases continuously for times greater than 3 seconds.

• The graph is linear, and it decreases continuously for times less than 3 seconds and increases continuously for times greater than 3 seconds.

• The graph is linear, and it increases continuously for times less than 3 seconds and decreases continuously for times greater than 3 seconds.

Answer explanation

The graph is non-linear, showing a decrease in height before 3 seconds as the rocket ascends, and an increase after 3 seconds as it descends. This matches the correct choice, indicating the behavior of the rocket's flight.

Answer explanation

The correct choice is y=(y2-y1)/(x2-x1)x+b. This formula calculates the slope (m) of the line using the coordinates of points (x1,y1) and (x2,y2) and includes the y-intercept (b), forming the equation of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

George graphs a relation that is not a function. Which of these could represent his graph?

• 
• 
• 
• 

Answer explanation

This is the result of recognizing that since each member of the domain, except for –6, is assigned to two members of the range, this relation does not represent a function. In other words, since the graph fails the vertical line test, it does not represent a function.

Which of these sets of ordered pairs are functions?

R = {(0, 0), (1, 1), (2, 2)}

S = {(0, 1), (1, 2), (2, 3)}

T = {(0, 1), (0, 2), (0, 3)}

• only set S

• only sets R and S

• only sets S and T

• sets R, S and T

Answer explanation

A function must have unique outputs for each input. Sets R and S have unique outputs (0, 1, 2) for their inputs. Set T has multiple outputs (1, 2, 3) for the input 0, so it is not a function. Thus, only sets R and S are functions.

Tags

CCSS.8.F.A.1

In order to play in chess tournaments at the Marshall Club, Malik pays a fee to become a member. In addition, he pays a set rate for each tournament in which he competes. After competing in 4 tournaments Malik has paid a total of $85, and after competing in 7 tournaments he has paid a total of $130. Malik's friend Masai gets a discount on membership to the Marshall Club and pays $10 less for the membership fee than Malik. Which linear equation gives the total price, p, Masai will pay to compete in t tournaments at the Marshall Club?

• p = 5t + 15

• p = 15t + 25

• p = 15t + 15

• p = 5t + 25

Answer explanation

Malik's total cost after 4 tournaments is $85, giving a membership fee of $15 and a tournament fee of $15 each. Masai pays $10 less for membership, so his total cost is p = 15t + 15.

Tags

CCSS.8.EE.C.7B

A local farm deposits 1.5 ft³ of fertilizer into a storage container at a garden store each week. After 5 weeks the container has 15 ft³ of fertilizer. If it takes 14 more weeks for the storage container to be filled, what is the capacity of the storage container?

• 21 ft³

• 36 ft³

• 28.5 ft³

• 43.5 ft³

Answer explanation

The farm deposits 1.5 ft³ weekly. In 5 weeks, that's 7.5 ft³. After 14 more weeks (21 ft³ total), the container holds 28.5 ft³. Adding the initial 15 ft³ gives a total capacity of 43.5 ft³.

Tags

CCSS.HSF.BF.A.2

Which of these functions has a y-intercept that is greater than that of the linear function represented by the table of values below, and why?

• y = x + 9 , because the y-intercept of the function represented by the table of values is 2

• y = x + 9 , because the y-intercept of the function represented by the table of values is 5

• y = 8x + 1, because the y-intercept of the function represented by the table of values is 2

• y = 8x + 1, because the y-intercept of the function represented by the table of values is 5

Answer explanation

The function y = 8x + 1 has a y-intercept of 1, which is greater than the y-intercept of the function represented by the table of values, which is 2. Therefore, this choice is correct.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The graph models the speed of a 40-minute run that Tara completed.
Tara wrote a set of statements that may or may not be true about her run. Classify the following statement as True or False.

Statement 1: Tara ran the fastest at the end of her run.

• True

• False

Answer explanation

The graph indicates that Tara's speed increased towards the end of her run, confirming that she ran the fastest at that point. Therefore, Statement 1 is True.

Tags

CCSS.HSF.IF.B.4