Question

is the function described by the points in this table linear or nonlinear?
options: nonlinear, linear
table:

x	y
-3	-5
-1	-1
0	1
1	3
3	7

Explanation:

Step1: Calculate slope between first two points

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-3, -5)$ and $(-1, -1)$:
$m_1 = \frac{-1 - (-5)}{-1 - (-3)} = \frac{4}{2} = 2$

Step2: Calculate slope between second and third points

For points $(-1, -1)$ and $(0, 1)$:
$m_2 = \frac{1 - (-1)}{0 - (-1)} = \frac{2}{1} = 2$

Step3: Calculate slope between third and fourth points

For points $(0, 1)$ and $(1, 3)$:
$m_3 = \frac{3 - 1}{1 - 0} = \frac{2}{1} = 2$

Step4: Calculate slope between fourth and fifth points

For points $(1, 3)$ and $(3, 7)$:
$m_4 = \frac{7 - 3}{3 - 1} = \frac{4}{2} = 2$
All slopes are equal (2), so the function is linear.

Answer:

linear