Question

(Slope-Intercept Form MC)

Which equation represents the graph?

a graph of a line that passes through the points 0 comma negative 2 and negative 2 comma 2

y equals negative 2 times x plus one half
y equals negative one-half times x plus one half
y = −2x − 2
y equals negative one-half times x minus 2
Question 2(Multiple Choice Worth 5 points)

(Slope MC)

What is the slope of the linear relationship shown on the graph?

a graph of a line that passes through the points 0 comma negative 2 and negative 2 comma 1

negative two thirds
two thirds
negative three halves
three halves
Question 3(Multiple Choice Worth 5 points)

(Systems of Linear Equations MC)

Which graph shows the solution to the system of linear equations?

y equals one third times x

x + 3y = 6

coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1
coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1
coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1
coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3
Question 4(Multiple Choice Worth 5 points)

(Systems of Linear Equations LC)

Determine the number of solutions to the system of linear equations shown on the graph.

coordinate plane with one line that passes through the points negative 1 comma 4 and 0 comma 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 3

One solution at (1, −2)
One solution at (−2, 1)
Infinitely many solutions
No solution
Question 5(Multiple Choice Worth 5 points)

(Systems of Linear Equations MC)

Which point is a solution to the system of linear equations?

y = −x + 3

x − 3y = 15?

(−1, 5)
(0, 3)
(3, 0)
(6, −3)
Question 6(Multiple Choice Worth 5 points)

(Slope MC)

Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $60, plus $28 per hour. What is the slope of this situation?

28
32
60
88
Question 7(Multiple Choice Worth 5 points)

(Slope-Intercept Form MC)

A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 14 inches long and is melting at a rate of 0.9 inches per hour. Find and interpret the slope for this relationship.

−0.9; for every additional hour, the length of the icicle decreases by 0.9 inches
0.9; for every additional hour, the length of the icicle increases by 0.9 inches
−14; the length of the icicle when the student first measures it
14; the length of the icicle when the student first measures it
Question 8(Multiple Choice Worth 5 points)

(Graphing Linear Equations MC)

A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.


Restaurant
Number of Side Dishes Total Cost
2 $8.50
4 $11.50
5 $13.00
8 $17.50


Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13
Question 9(Multiple Choice Worth 5 points)

(Systems of Linear Equations MC)

The system of linear equations 3x + 2y = −4 and y equals one half times x plus 1 is graphed on a coordinate plane. Approximate the solution to the system.

coordinate plane with one line that passes through the points 0 comma negative 2 and negative 2 comma 1 and another line that passes through the points 0 comma 1 and 2 comma 2

(−1.5, 0.25)
(−0.5, 0.75)
(1.5, 0.25)
(−2.5, 1.5)

Answer 1

This answer provides step-by-step explanations for nine multiple-choice questions covering various mathematical topics such as slope-intercept form, systems of linear equations, and graphing linear equations.

Step-by-step explanation:

Question 1:

The equation that represents the graph of a line passing through the points (0, -2) and (-2, 2) is y = -1/2x + 1/2.

Question 2:

The slope of the linear relationship shown on the graph passing through (0, -2) and (-2, 1) is -2/3.

Question 3:

The graph that shows the solution to the system of linear equations y = 1/3x and x + 3y = 6 is the coordinate plane with one line passing through (0, 2) and (-3, 3), and another line passing through (0, 0) and (-3, -1).

Question 4:

The system of linear equations shown on the graph has no solution.

Question 5:

The point (-1, 5) is a solution to the system of linear equations y = -x + 3 and x - 3y = 15.

Question 6:

The slope of the situation in Superior Segway Tours charging $60 one-time fee and $28 per hour is 28.

Question 7:

The slope of the relationship between the length of the icicle and time is -0.9.

Question 8:

The graph that shows the relationship between the number of side dishes and the total cost is the one with a line going from (0, 5.25) through (3, 9.75).

Question 9:

The approximate solution to the system of linear equations 3x + 2y = -4 and y = 1/2x + 1 is (-1.5, 0.25).