Question

the table shows a function. is the function linear or nonlinear?
x | -4 | 3 | 10
y | 0 | -7 | -10
linear
nonlinear

Explanation:

Step1: Calculate Δx between points

$\Delta x_1 = 3 - (-4) = 7$, $\Delta x_2 = 10 - 3 = 7$

Step2: Calculate Δy between points

$\Delta y_1 = -7 - 0 = -7$, $\Delta y_2 = -10 - (-7) = -3$

Step3: Check slope consistency

Slope 1: $\frac{\Delta y_1}{\Delta x_1} = \frac{-7}{7} = -1$
Slope 2: $\frac{\Delta y_2}{\Delta x_2} = \frac{-3}{7}$

Answer:

nonlinear