Question

write the linear equation that gives the rule for this table.

x	y
5	8
6	20
7	32

write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(4,-4)$ and $(5,8)$. Then $m=\frac{8-(-4)}{5 - 4}=\frac{8 + 4}{1}=12$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(4,-4)$ and $m = 12$, we have $y-(-4)=12(x - 4)$.

Step3: Simplify the equation

$y + 4=12x-48$. Then $y=12x-52$.

Answer:

$y = 12x-52$