A local movie theater found that if the admission was $13, the attendance was about 1900 customers per day. When the price of admission was dropped to $7, attendance increased to about 3000 per day. Write a linear equation for the attendance in terms of price, p. (A=mp+b)
Ok this is what i got
A-3000-1900/7-13
= -550/3
A-1900=-550/3(P-13)
A-1900=-550/3P+7150/3
And it says the answer is
-550/3p+12850/3
I'm confused with how they got 12850/3 instead of 9050/3 because if you add 1900 and 7150 that's what u get..
thanks in advance
let's take it from
A-1900=-550/3(P-13) , which is correct
I usually try to eliminate my fractions, so I will multiply by 3
3A - 5700 = -550(P-13)
3A - 5700 = -550P + 7150
3A = -550P + 7150 + 5700
3A = -550P + 12850
A = (-550/3)P + 12850/3
To determine the linear equation for attendance in terms of price, we can use the given points (13, 1900) and (7, 3000).
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (3000 - 1900) / (7 - 13)
= 1100 / -6
= -550/3
Now let's find the y-intercept (b) by substituting one of the points and the slope into the equation:
1900 = (-550/3)(13) + b
b = 1900 + 550/3(13)
b = 1900 + 7150/3
b = (1900*3 + 7150)/3
b = 12850/3
Therefore, the equation for attendance (A) in terms of price (p) is:
A = (-550/3)p + 12850/3
The answer you were given (A = -550/3p + 12850/3) is indeed correct. The value 12850/3 represents the y-intercept, which is the value of A when p = 0. It is found by adding the constant term of 1900 to the calculated value of b, which is 7150/3. Thus, the correct equation is A = -550/3p + 12850/3.