Answer
11x + y = 40
Explanation
We know from our table that when Mary has seen 0 movies her budget is $40, so our first point is (0, 40)
We also know that when she has seen 1 movie her budget is $29, so our second point is (1, 29)
To find our line equation, we first need to find the slope between our points. To do it, we are using the slope formula: \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
where
\((x_{1},y_{1})\) are the coordinates of the first point
\((x_{2},y_{2})\) are the coordinates of the second point
We can infer from our points that \(x_{1}=0\), \(y_{1}=40\), \(x_{2}=1\), and \(y_{2}=29\). So let's replace those values in our formula to find \(m\)
\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
\(m=\frac{29-40}{1-0}\)
\(m=-11\)
Now that we have our slope, we can use the point slope formula to find the equation of our line
\(y-y_{1}=m(x-x_{1})\)
\(y-40=-11(x-0)\)
\(y-40=-11x\)
\(y=-11x+40\)
\(y+11x=40\)
\(11x+y=40\)
