Question

write the linear equation that gives the rule for this table. 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 $(2,0)$ and $(3,1)$. Then $m=\frac{1 - 0}{3 - 2}=1$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know $m = 1$ and we can use the point $(2,0)$. Substitute $x = 2$, $y=0$ and $m = 1$ into $y=mx + b$. So $0=1\times2 + b$, which gives $b=-2$.

Answer:

$y=x - 2$