find the equation of the linear function represented by the table below in slope - intercept form.

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(2,1)$. Then $m=\frac{1 - 3}{2 - 1}=\frac{-2}{1}=-2$.

Step2: Find the y - intercept

The slope - intercept form is $y = mx + b$. Substitute $m=-2$, $x = 1$ and $y = 3$ into the equation: $3=-2\times1 + b$. Solving for $b$ gives $b=3 + 2=5$.

Answer:

$y=-2x + 5$