To determine the correct equation modeling the total profit, \( y \), based on the number of magazines sold, \( x \), given two points \((x_1, y_1)\) = (60, 220) and \((x_2, y_2)\) = (100, 420), follow these steps:
1. Calculate the slope (rate of change of profit per magazine) \( m \):
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the given points:
[tex]\[
m = \frac{420 - 220}{100 - 60} = \frac{200}{40} = 5
\][/tex]
So, the slope \( m \) is 5.
2. Determine the equation in point-slope form:
The point-slope form of the equation of a line is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the point (60, 220) and the slope 5:
[tex]\[
y - 220 = 5(x - 60)
\][/tex]
3. Identify the correct equation from the given choices:
The correct equation matches the point-slope form we derived. Comparing:
[tex]\[
y - 220 = 5(x - 60)
\][/tex]
We find that this matches choice B.
Thus, the equation that models the total profit \( y \) based on the number of magazines sold \( x \) is:
[tex]\[
\boxed{y - 220 = 5(x - 60)}
\][/tex]
The correct answer is:
B. [tex]\( y - 220 = 5(x - 60) \)[/tex]
