Question

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

x	y
6	46
7	47
8	48

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 the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(5,45)$ and $(x_2,y_2)=(6,46)$. Then $m=\frac{46 - 45}{6 - 5}=1$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. Substitute $m = 1$, $x = 5$ and $y = 45$ into the equation: $45=1\times5 + b$. Solving for $b$, we get $b=45 - 5=40$.

Answer:

$y=x + 40$