Question

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

x	y
3	0
4	1
5	2
6	3

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 $(3,0)$ and $(4,1)$. Then $m=\frac{1 - 0}{4 - 3}=1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(3,0)$ and $m = 1$, we have $y-0=1\times(x - 3)$.

Step3: Simplify the equation

Simplifying $y-0=1\times(x - 3)$ gives $y=x - 3$.

Answer:

$y=x - 3$