3. Dr. Ellison says that the equation y = -3x + 7 has a solution of (2, 13). Is Dr. Ellison right or wrong?

Question

A) More information is needed to answer this question.
B) Dr. Ellison is wrong.
C) Dr. Ellison is right.

4. A satellite tv company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y = 99x + 15. Which statement represents the meaning of each part of the function?
A) y is the total cost, x is the number of months of service, $99 is the installation fee, and $15 is the service charge per month.
B) x is the total cost, y is the number of months of service, $15 is the installation fee, and $99 is the service charge per month.
C) y is the total cost, x is the number of months of service, $15 is the installation fee, and $99 is the service charge per month.
D) x is the total cost, y is the number of months of service, $99 is the installation fee, and $15 is the service charge per month.

5. What is the rate of change of the table below?
X: 1, 2, 3, 4, 5, 6
Y: 12, 19, 26, 33, 40, 47
A) -12
B) 12
C) 1/7
D) 7

7. What is the correct set up to finding the slope of a line that passes through the points (6, −3) and (−2, 7)?
A) 6 - 2 / -3 + 7
B) 6 - (-3) / -2 - 7
C) 7 - (-3) / -2 - 6
D) 7 - 3 / -2 - 6

8. Which equation of a line is parallel to the equation -4x + 3y = 12?
A) y = 3x + 12
B) y = −4/3x + 4
C) y = 4/3x + 6
D) y = 4x + 8

Answer 1

Let's answer each question one by one:

3. Dr. Ellison says that the equation y = -3x + 7 has a solution of (2, 13). Is Dr. Ellison right or wrong? To check if (2, 13) is a solution, we substitute x = 2 into the equation: y = -3(2) + 7 y = -6 + 7 y = 1

Since the output is 1 (not 13), Dr. Ellison is wrong. Answer: B) Dr. Ellison is wrong.

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4. A satellite TV company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y = 99x + 15. Which statement represents the meaning of each part of the function? In the equation, y represents total cost, x represents the number of months of service, $99 is the installation fee, and $15 is the monthly service charge. Answer: A) y is the total cost, x is the number of months of service, $99 is the installation fee, and $15 is the service charge per month.

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5. What is the rate of change of the table below? To find the rate of change, we look at the change in y over the change in x. The change in Y from 12 to 19 (increase of 7) occurs as x increases from 1 to 2 (increase of 1).

Rate of change = (change in Y) / (change in X) = (19 - 12) / (2 - 1) = 7 / 1 = 7. Answer: D) 7

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7. What is the correct setup to finding the slope of a line that passes through the points (6, −3) and (−2, 7)? The formula for the slope \( m \) between two points (x1, y1) and (x2, y2) is: \[ m = \frac{y2 - y1}{x2 - x1} \] Let (x1, y1) = (6, -3) and (x2, y2) = (-2, 7). So, \[ m = \frac{7 - (-3)}{-2 - 6} = \frac{7 + 3}{-2 - 6} = \frac{10}{-8} = -\frac{5}{4} \]

To match the choices provided: Using the formula setup: \[ y2 - y1 = 7 - (-3) \] and \[ x2 - x1 = -2 - 6 \]

Thus, the correct expression for the slope setup is: Answer: C) 7 - (-3) / -2 - 6

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8. Which equation of a line is parallel to the equation -4x + 3y = 12? To find a parallel line, we need to determine the slope of the given line. First, we rewrite the equation in slope-intercept form (y = mx + b): 3y = 4x + 12 y = (4/3)x + 4

The slope of this line is 4/3. Lines that are parallel have the same slope. We then look for a line with a slope of 4/3 from the choices given:

• A) y = 3x + 12 (slope = 3)
• B) y = −4/3x + 4 (slope = -4/3)
• C) y = 4/3x + 6 (slope = 4/3)
• D) y = 4x + 8 (slope = 4)

The only one with a slope of 4/3 is: Answer: C) y = 4/3x + 6