Question

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

$x$	$y$
2	$-5$
3	$-7$
4	$-9$

Explanation:

Step1: Calculate the slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(1,-3)$ and $(x_2,y_2)=(2,-5)$:
$m=\frac{-5-(-3)}{2-1}=\frac{-2}{1}=-2$

Step2: Find y-intercept $b$

Substitute $m=-2$, $x=1$, $y=-3$ into $y=mx+b$:
$-3 = (-2)(1)+b$
Solve for $b$: $b=-3+2=-1$

Step3: Write slope-intercept equation

Substitute $m=-2$ and $b=-1$ into $y=mx+b$:
$y=-2x-1$

Answer:

$y=-2x-1$