Question

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

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

Explanation:

Step1: Calculate the slope

The slope $m$ of a line is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(3,5)$ and $(x_2,y_2)=(4,6)$. Then $m=\frac{6 - 5}{4 - 3}=1$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with $m = 1$ and the point $(3,5)$. Substitute into the equation: $y-5=1\times(x - 3)$. Expand to get $y-5=x - 3$. Then $y=x+2$.

Answer:

$y=x + 2$