Question

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

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,0)$ and $(x_2,y_2)=(2, - 2)$. Then $m=\frac{-2 - 0}{2 - 1}=\frac{-2}{1}=-2$.

Step2: Find the y - intercept

Use the slope - intercept form $y=mx + b$ and substitute $m=-2$, $x = 1$, and $y = 0$. So $0=-2\times1 + b$. Solving for $b$ gives $b = 2$.

Step3: Write the equation

The equation of the line in slope - intercept form is $y=-2x + 2$.

Answer:

$y=-2x + 2$