Question

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

x	y
2	-5
3	-9
4	-13

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1, - 1)$ and $(x_2,y_2)=(2,-5)$. Then $m=\frac{-5-(-1)}{2 - 1}=\frac{-5 + 1}{1}=-4$.

Step2: Find the y - intercept

The slope - intercept form is $y=mx + b$. Substitute $m=-4$, $x = 1$ and $y=-1$ into the equation: $-1=-4\times1 + b$. Solve for $b$: $b=-1+4 = 3$.

Answer:

$y=-4x + 3$