Question

8.F.2: Functions W and Z are both linear functions of x. Which statement comparing the functions is true? Select ALL that apply.

A. The slope of Function W is less than the slope of Function Z.

B. The slope of Function W is greater than the slope of Function Z.

C. The slope of Function W is equal to the slope of Function Z.

D. The y-intercept of Function W is less than the y-intercept of Function Z.

E. The y-intercept of Function W is equal to the y-intercept of Function Z.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

Answer 1

Answer: B and F

Explanation:

Answer 2

*the graph of Function W and table of values of Function Z are in the diagram attached below.

Answer:

B. The slope of Function W is greater than the slope of Function Z.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

Explanation:

To determine which of the statements compare both functions correctly, let's find the slope (m) and the y-intercept (b) of each function given.

✍️Function W:

Slope of Function B, using two points on the line, (0, -1) and (2, 0):

`m = (y_2 - y_1)/(x_2 - x_1) = (0 -(-1))/(2 - 0) = (1)/(2) = 0.5`

✅Slope = 0.5.

y-intercept is the point at which the line intercepts the y-axis. Therefore, the y-intercept, b = -1. The line cuts the y-axis at y = -1. At this point, x = 0.

✅y-intercept = -1.

✍️Function Z:

Slope of Function Z, using two pairs of values from the table of values for function Z, (0, -2) and (2, -1.5):

`m = (y_2 - y_1)/(x_2 - x_1) = (-1.5 -(-2))/(2 - 0) = (0.5)/(2) = 0.25`

✅Slope = 0.25.

y-intercept is the value of y when x = 0. It is at this point the line of the function of X intercepts the y-axis. From the table given, we can see that when x = 0, y = -2. Therefore:

✅y-intercept = -2.

Thus, the following statements that compares both functions are TRUE:

B. The slope of Function W is greater than the slope of Function Z.

✔️This is TRUE because 0.5 is greater than 0.25.

F. The y-intercept of Function W is greater than the y-intercept of Function Z.

✔️This is TRUE because -1 is greater than -2.