Question

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

x	y
1	0
2	-5
3	-10
4	-15

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 $(x_2,y_2)=(2, - 5)$. Then $m=\frac{-5 - 0}{2 - 1}=\frac{-5}{1}=-5$.

Step2: Find the y - intercept

Use the slope - intercept form $y = mx + b$ and substitute $m=-5$, $x = 1$ and $y = 0$. We get $0=-5\times1 + b$. Solving for $b$: $b=5$.

Answer:

$y=-5x + 5$