Question

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

x	y
8	1
9	2
10	7

options: linear, nonlinear

Explanation:

Step1: Calculate the first slope

To determine if a function is linear, we check the slope between consecutive points. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For the first two points $(8, 1)$ and $(9, 2)$:
$m_1 = \frac{2 - 1}{9 - 8} = \frac{1}{1} = 1$

Step2: Calculate the second slope

For the next two points $(9, 2)$ and $(10, 7)$:
$m_2 = \frac{7 - 2}{10 - 9} = \frac{5}{1} = 5$

Step3: Compare the slopes

Since $m_1 = 1$ and $m_2 = 5$, and $1
eq 5$, the slopes are not equal. A linear function has a constant slope, so this function is nonlinear.

Answer:

nonlinear