Question

The description below represents Function A and the table represents Function B:

Function A

The function is 2 more than 5 times x.

Function B

x y
−1 2
0 5
1 8
Which statement is correct about the slope and intercept of the two functions?

A) Their slopes are equal but y-intercepts are not equal.

B) Their slopes are not equal but y-intercepts are equal.

C) Both slopes and y-intercepts are equal.

D) Neither slopes nor y-intercepts are equal.

Answer 1

D is correct

Explanation:

Step 1 : Find equation of function A in y = mx + c

2 more than 5 times x

f(x) = 2 + 5x or y = 5x + 2

Step 2 : Identify slope and y-intercept of function A

y = mx + c

y = 2 + 5x

Slope = m = 5

Y-intercept = c = 2

Step 3 : Find the equation of function B in y = mx + c

From my understanding, the number given in the question are coordinates

(-1, 2) , (0, 5) , (1, 8)

Slope = y2-y1/x2-x1

Lets take two coordinates : (-1, 2) , (0, 5)

Slope = 5-2/0-(-1)

Slope = 3/1 = 3

For y-intercept

Lets take (1, 8)

y = mx + c

8 = 3(1) + c

c = 5

The equation is f(x) = 3x + 5 or y = 3x + 5

Step 4 : Lets write both equations with their slope and y-intercept and check with the statements

y = 5x + 2

y = 3x + 5

A) Their slopes are equal but y-intercepts are not equal. Incorrect

B) Their slopes are not equal but y-intercepts are equal. Incorrect

C) Both slopes and y-intercepts are equal. Incorrect

D) Neither slopes nor y-intercepts are equal. Correct

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