Question

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

x	y
2	4
3	6
4	8
5	10

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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take $(x_1,y_1)=(2,4)$ and $(x_2,y_2)=(3,6)$. Then $m=\frac{6 - 4}{3 - 2}=\frac{2}{1}=2$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. We know $m = 2$, and we can substitute one of the points, say $(2,4)$ into the equation. So $4=2\times2 + b$. Simplifying gives $4 = 4 + b$, and $b = 0$.

Answer:

$y = 2x$