Given:
a.) If the price of admission was $10, the attendance was about 1150 customers per day.
b.) When the price of admission was dropped to $6, attendance increased to about 1900 per day.
Let's generate the linear equation where:
x, y = p, A
m = slope
b = the y-intercept
We get,
Step 1: Let's determine the slope.
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{A_2-A_1}{p_2-p_1}[/tex][tex]\text{ = }\frac{\text{ 1900 - 1150}}{\text{ 6 - 10}}[/tex][tex]\text{ = }\frac{\text{ 750}}{-4}[/tex][tex]\text{ m = -}\frac{375\text{ }}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute p, A = 10, 1150 and m = -375/2 in A = mp + b
[tex]\text{ A = mp + b}[/tex][tex]\text{ 1150 = (}-\frac{375}{2})(10)\text{ + b}[/tex][tex]\text{ 1150 = -}\frac{3750}{2}\text{ + b}[/tex][tex]\text{ 1150 = -1875 + b}[/tex][tex]\text{ b = 1150 + 1875}[/tex][tex]\text{b = }3025[/tex]Step 3: Let's complete the equation. Substitute m = -375/2 and b = 3025 in A = mp + b
[tex]\text{ A = mp + b}[/tex][tex]\text{ = (-}\frac{375}{2})p\text{ + (3025)}[/tex][tex]\text{ A = -}\frac{375}{2}p\text{ + 3025}[/tex]Therefore, the linear equation for the attendance in terms of the price, p, is:
[tex]\text{ A = -}\frac{375}{2}p\text{ + 3025}[/tex]