Question

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

Explanation:

Step1: Convert mixed numbers to decimals

$-7\frac{1}{5}=-7.2$, $-5\frac{1}{2}=-5.5$, $8\frac{1}{2}=8.5$, $9\frac{4}{5}=9.8$

Step2: Calculate first slope (m1)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m_1=\frac{-7 - (-7.2)}{-5.5 - (-6)}=\frac{0.2}{0.5}=0.4$

Step3: Calculate second slope (m2)

$m_2=\frac{9.8 - (-7)}{8.5 - (-5.5)}=\frac{16.8}{14}=1.2$

Step4: Compare slopes

Linear functions have constant slopes. $0.4
eq1.2$

Answer:

nonlinear