Question

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

x	y
3	28
4	35
5	42
6	49

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 is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(3,28)$ and $(x_2,y_2)=(4,35)$. Then $m=\frac{35 - 28}{4 - 3}=\frac{7}{1}=7$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Using the point $(3,28)$ and $m = 7$, we have $y-28=7(x - 3)$. Expand the right side: $y-28=7x-21$. Add 28 to both sides to get $y=7x + 7$.

Answer:

$y = 7x+7$