Question

the table shows a function. is the function linear or nonlinear?

x	y
-7	5
0	12
7	19

options: linear, nonlinear

Explanation:

Step1: Calculate the slope between the first two points

The formula for slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For the points $(-7, 5)$ and $(0, 12)$, we have $x_1 = -7$, $y_1 = 5$, $x_2 = 0$, $y_2 = 12$. So the slope $m_1 = \frac{12 - 5}{0 - (-7)} = \frac{7}{7} = 1$.

Step2: Calculate the slope between the last two points

For the points $(0, 12)$ and $(7, 19)$, we have $x_1 = 0$, $y_1 = 12$, $x_2 = 7$, $y_2 = 19$. The slope $m_2 = \frac{19 - 12}{7 - 0} = \frac{7}{7} = 1$.

Step3: Compare the slopes

Since $m_1 = m_2 = 1$, the rate of change (slope) is constant. A function with a constant slope is linear.

Answer:

linear