Question

A student decided to use the points (.5, 20) and (3, 150) to make what she believed was a better regression equation. Her answer was f(x)=52x+4. The family decides to extend the yard sale to be 10 hours long. How much money can they expect to make.

Answer 1

Answer:

They can expect to make $524

Step-by-step explanation:

Lets solve the problem

The form of the linear function is f(x) = m x + b, where m is the slope of the line and b is the y-intercept (value f(x) at x = 0)

∵ The student decided to use the points (0.5, 20) and (3, 150)

   to make a better regression equation

- She calculated the slope of the line using the two points

∵ $m=\frac{150-20}{3-0.5}=52$

- She substituted the value of m in the form above

∴ f(x) = 52 x + b

- Than she find that the best value of f(x) at x = 0 is 4

∴ f(x) = 52 x + 4

∵ x represents the number of hours

∵ y represents the money

∵ The family decides to extend the yard sale to be 10 hours long

- That means substitute x by 10 in f(x)

∵ x = 10

∴ f(10) = 52(10) + 4

∴ f(10) = 520 + 4

∴ f(10) = 524

∴ They can expect to make $524