Answer :
To find the correct equation that models the total profit, [tex]\( y \)[/tex], based on the number of magazines sold, [tex]\( x \)[/tex], we can use the given points: (60 magazines, [tex]$220 profit) and (100 magazines, $[/tex]420 profit).
1. Determine the slope (m) of the line:
The slope formula is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the values from the points (60, 220) and (100, 420):
[tex]\[
m = \frac{420 - 220}{100 - 60} = \frac{200}{40} = 5
\][/tex]
So, the slope, [tex]\( m \)[/tex], is 5.
2. Use the point-slope form to write the equation:
The point-slope form of a line is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the point (60, 220) and the slope [tex]\( m = 5 \)[/tex]:
[tex]\[
y - 220 = 5(x - 60)
\][/tex]
This is the equation that models the relationship between the profit, [tex]\( y \)[/tex], and the number of magazines sold, [tex]\( x \)[/tex].
The correct choice from the options provided is:
B. [tex]\( y-220=5(x-60) \)[/tex].
1. Determine the slope (m) of the line:
The slope formula is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the values from the points (60, 220) and (100, 420):
[tex]\[
m = \frac{420 - 220}{100 - 60} = \frac{200}{40} = 5
\][/tex]
So, the slope, [tex]\( m \)[/tex], is 5.
2. Use the point-slope form to write the equation:
The point-slope form of a line is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Using the point (60, 220) and the slope [tex]\( m = 5 \)[/tex]:
[tex]\[
y - 220 = 5(x - 60)
\][/tex]
This is the equation that models the relationship between the profit, [tex]\( y \)[/tex], and the number of magazines sold, [tex]\( x \)[/tex].
The correct choice from the options provided is:
B. [tex]\( y-220=5(x-60) \)[/tex].