Question

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

x	y
1	2
2	-1
3	-4
4	-7

Explanation:

Step1: Calculate the slope

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

Step2: Find the y - intercept

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

Answer:

$y=-3x + 5$