Question

x -8 -6 -4 -2
y -5 -15 -45 -135
is the relationship linear, exponential, or neither?
choose 1 answer:
a linear
b exponential
c neither

Explanation:

Step1: Check linearity (constant y-differences)

Calculate differences between consecutive $y$-values:
$\Delta y_1 = -15 - (-5) = -10$
$\Delta y_2 = -45 - (-15) = -30$
$\Delta y_3 = -135 - (-45) = -90$
The differences are not constant, so not linear.

Step2: Check exponential (constant y-ratios)

Calculate ratios of consecutive $y$-values:
$r_1 = \frac{-15}{-5} = 3$
$r_2 = \frac{-45}{-15} = 3$
$r_3 = \frac{-135}{-45} = 3$
The ratios are constant, so it is exponential.

Answer:

B. Exponential