Answer:
[tex] y = -3,000x + 15,000 [/tex]
Explanation:
A linear relationship is usually represented by the equation, [tex] y = mx + b [/tex], where m = slope, and b = y-intercept.
Find m and b to derive an equation that describes the relationship between x and y.
Hours since 4 p.m is the x-variable and number of tickets remaining is the y-variable.
Using two coordinate pairs, (3, 6,000) and (4, 3,000), find the slope (m):
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6,000 - 3,000}{3 - 4} = \frac{3,000}{-1} [/tex]
Slope (m) = -3,000
Substitute x = 5, y = 0, and m = -3,000 into [tex] y = mx + b [/tex], to find the value of b. (Note that you can the value of any coordinate pair as x and y. You'd get the same value of b)
[tex] 0 = (-3,000)(5) + b [/tex]
[tex] 0 = -15,000 + b [/tex]
Add 15,000 to both sides
[tex] 15,000 = b [/tex]
[tex] b = 15,000 [/tex]
Substitute b = 15,000 and m = -3,000 into [tex] y = mx + b [/tex], to get the equation that describes the relationship between x and y.
[tex] y = -3,000x + 15,000 [/tex]
