when the price for admission to a sporting event was $100 per ticket, 50000 people attended the event. When the price increased to $108, the attendance decreased to 45000 people. Which linear equation represents the attendance (d) in terms of the admission price (p)
2950
To find the linear equation representing the attendance (d) in terms of the admission price (p), we can use the given information.
We know that when the price for admission was $100 per ticket, 50,000 people attended the event. This gives us the point (100, 50,000).
We also know that when the price increased to $108, the attendance decreased to 45,000 people. This gives us the point (108, 45,000).
To find the equation of the line passing through these two points, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
Where:
- y and x represent the coordinates of a point on the line.
- m represents the slope of the line.
- b represents the y-intercept (the value of y when x is equal to 0).
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values from the given points, we get:
m = (45,000 - 50,000) / (108 - 100)
= -5,000 / 8
= -625
Now, let's find the y-intercept (b) by substituting one of the points into the slope-intercept form:
50,000 = -625 * 100 + b
50,000 = -62,500 + b
b = 50,000 + 62,500
b = 112,500
Therefore, the linear equation representing the attendance (d) in terms of the admission price (p) is:
d = -625p + 112,500