write the linear equation that gives the rule for this table.\nwrite your answer as an equation with y…

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 $(x_1,y_1)=(2,43)$ and $(x_2,y_2)=(3,47)$. Then $m=\frac{47 - 43}{3 - 2}=\frac{4}{1}=4$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(2,43)$ and $m = 4$, we have $y-43=4(x - 2)$.

Step3: Convert to slope - intercept form

Expand the right side: $y-43=4x-8$. Then add 43 to both sides to get $y=4x + 35$.

Answer:

$y = 4x+35$