Answer :
To solve this problem, we need to find an equation that models the total profit [tex]\( y \)[/tex] based on the number of magazines sold [tex]\( x \)[/tex].
We have two key pieces of information:
1. When 60 magazines were sold, the profit was [tex]$220.
2. When 100 magazines were sold, the profit was $[/tex]420.
These are two points on a graph: [tex]\((60, 220)\)[/tex] and [tex]\((100, 420)\)[/tex].
### Step 1: Find the Slope
To find the equation of the line, we first calculate the slope [tex]\( m \)[/tex]. The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substitute the given values:
[tex]\[ m = \frac{420 - 220}{100 - 60} = \frac{200}{40} = 5 \][/tex]
### Step 2: Use the Point-Slope Form
With the slope [tex]\( m = 5 \)[/tex], we can use the point-slope form of a line equation, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Let's use the point [tex]\((60, 220)\)[/tex]:
[tex]\[ y - 220 = 5(x - 60) \][/tex]
This equation represents the relationship between the number of magazines sold [tex]\( x \)[/tex] and the total profit [tex]\( y \)[/tex].
Thus, the correct equation from the given options is:
A. [tex]\( y - 220 = 5(x - 60) \)[/tex]
We have two key pieces of information:
1. When 60 magazines were sold, the profit was [tex]$220.
2. When 100 magazines were sold, the profit was $[/tex]420.
These are two points on a graph: [tex]\((60, 220)\)[/tex] and [tex]\((100, 420)\)[/tex].
### Step 1: Find the Slope
To find the equation of the line, we first calculate the slope [tex]\( m \)[/tex]. The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substitute the given values:
[tex]\[ m = \frac{420 - 220}{100 - 60} = \frac{200}{40} = 5 \][/tex]
### Step 2: Use the Point-Slope Form
With the slope [tex]\( m = 5 \)[/tex], we can use the point-slope form of a line equation, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Let's use the point [tex]\((60, 220)\)[/tex]:
[tex]\[ y - 220 = 5(x - 60) \][/tex]
This equation represents the relationship between the number of magazines sold [tex]\( x \)[/tex] and the total profit [tex]\( y \)[/tex].
Thus, the correct equation from the given options is:
A. [tex]\( y - 220 = 5(x - 60) \)[/tex]
