Respuesta :
Given:
$10 price = 1000 customers per week.
$6 price = 2950 customers per week.
Let's write a linear equation for the attendance in terms of the price, p.
Apply the slope-intercept form:
y = mx + b
In this case, let's use the form:
A = mp + b
Where m is the average rate of change(slope) and b is the y-intercept.
To find the slope, m, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where:
(x1, y1) ==> (10, 1000)
(x2, y2) ==> (6, 2950)
Hence, we have:
[tex]m=\frac{2950-1000}{6-10}=\frac{1950}{-4}=-487.5[/tex]The average rate of change is -$487.5
To find the y-intercept, b, substitute either of the points for A and p, substitute -487.5 for x then evaluate.
Let's take the first point: (10, 1000)
A = mp + b
1000 = -487.5(10) + b
1000 = -4875 + b
Add 4875 to both sides:
1000 + 4875 = -4875 + 4875 + b
5875 = b
b = 5875
Therefore, the lineart equation for the attendance in terms of the price, p is:
A = -487.5p + 5875
ANSWER:
[tex]A=-487.5p+5875[/tex]