Question

question
find the equation of the linear function represented by the table below in slope-intercept form.
$x$ $y$
1 $-3$
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 $b$:
$-3 = -2 + b \implies b = -3 + 2 = -1$

Step3: Write slope-intercept equation

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

Answer:

$y = -2x - 1$