Certainly! To predict the number of coats Clothes-4You will sell at an outside temperature of [tex]$20^{\circ} F$[/tex], we can use a linear relationship given by the equation [tex]\( y = mx + c \)[/tex] where:
- [tex]\( x \)[/tex] is the temperature in degrees Fahrenheit,
- [tex]\( y \)[/tex] is the number of coats sold,
- [tex]\( m \)[/tex] is the slope of the line (rate at which the number of coats sold changes with temperature),
- [tex]\( c \)[/tex] is the y-intercept (number of coats sold when the temperature is 0 degrees Fahrenheit).
1. Substitute 20 for [tex]\( x \)[/tex] in the equation:
Plug [tex]\( x = 20 \)[/tex] degrees Fahrenheit into the equation [tex]\( y = mx + c \)[/tex].
2. Simplify to find the value for [tex]\( y \)[/tex]:
Given the linear relationship where the slope [tex]\( m \)[/tex] is [tex]\(-2\)[/tex], and the intercept [tex]\( c \)[/tex] is [tex]\(100\)[/tex], we substitute [tex]\( x = 20 \)[/tex]:
[tex]\[
y = -2(20) + 100
\][/tex]
3. Calculate the values:
Perform the multiplication first:
[tex]\[
-2 \times 20 = -40
\][/tex]
Then, add the result to the intercept:
[tex]\[
y = -40 + 100 = 60
\][/tex]
Finally, rounding to the nearest whole number, we find:
At [tex]\( 20^{\circ} F \)[/tex], about [tex]\( 60 \)[/tex] coats will be sold at Clothes-4You.
