question\nfind the equation of the linear function represented by the table below in slope - intercept form.

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1 = 1,y_1=-9)$ and $(x_2 = 2,y_2=-13)$. Then $m=\frac{-13-(-9)}{2 - 1}=\frac{-13 + 9}{1}=-4$.

Step2: Find the y - intercept

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m=-4$, and we can use a point from the table, say $(x = 1,y=-9)$. Substitute into $y=mx + b$: $-9=-4\times1 + b$. Solving for $b$ gives $b=-9 + 4=-5$.

Answer:

$y=-4x - 5$