Question

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

x	y
4	11
5	16
6	21

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

Explanation:

Step1: Find the slope (m)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(3,6)$ and $(x_2,y_2)=(4,11)$. Then $m=\frac{11 - 6}{4 - 3}=\frac{5}{1}=5$.

Step2: Find the y - intercept (b)

Use the point - slope form $y=mx + b$ and substitute $m = 5$, $x = 3$ and $y = 6$. So $6=5\times3 + b$. Solving for $b$ gives $b=6 - 15=- 9$.

Answer:

$y = 5x-9$