Question

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

x	y
3	6
4	16
5	26
6	36

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

Explanation:

Step1: Find the slope formula

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 the first two points $(3,6)$ and $(4,16)$. Then $m=\frac{16 - 6}{4 - 3}=\frac{10}{1}=10$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(3,6)$ and $m = 10$, we have $y-6=10(x - 3)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-6=10x-30$. Then add 6 to both sides to get $y = 10x-24$.

Answer:

$y = 10x-24$