Question

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

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1, - 3)$ and $(x_2,y_2)=(2,-5)$. Then $m=\frac{-5-(-3)}{2 - 1}=\frac{-5 + 3}{1}=-2$.

Step2: Find the y - intercept

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

Step3: Write the equation

The equation of the line in slope - intercept form is $y=-2x-1$.

Answer:

$y=-2x - 1$