Question

Which of the following represents a linear function with the same slope as the table below? *Select 2 that apply!
x f(x)
-4 14
-2 8
3 -7
5 -13

Answer 1

To determine the slope of the table, we can use the formula for slope:

slope = (change in y) / (change in x)

Using the table, we can calculate the slope for each pair of points:

slope between (-4, 14) and (-2, 8) = (8 - 14) / (-2 - (-4)) = -6 / 2 = -3
slope between (-2, 8) and (3, -7) = (-7 - 8) / (3 - (-2)) = -15 / 5 = -3
slope between (3, -7) and (5, -13) = (-13 - (-7)) / (5 - 3) = -6 / 2 = -3

We can see that all three pairs of points have the same slope of -3.

Now, let's look at the options:

A) f(x) = -3x + 1
B) f(x) = -2x + 1
C) f(x) = -x + 1
D) f(x) = -4x + 1

To have the same slope as the table, the linear function must have a coefficient of x equal to -3.

From the options, the linear functions that satisfy this condition are:

A) f(x) = -3x + 1
C) f(x) = -x + 1

Therefore, the correct answer is A) and C).