Question

Someone please help, 100 points.

1. The Cajun Heartland State Fair charges $1.25 per ticket for the rides. Johnny bought 25 tickets for the rides and spent a total of $43.75 at the fair. Johnny spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (Hint: linear equation should be written in slope- intercept form)
(c) Explain your answer to Part 1b.

A line goes through the points (9,8) and (4,-12).
What is the slope of the line? Show your work
Write the equation of the line in point-slope form. Show your work
Write the equation of the line in slope-intercept form. Show your work.

Answer 1

Part 1
Let:
y be the total cost
x be the number of tickets
a be fair admission

Since the fair charges $1.25 per ticket, the equation of the line would look like:

y = 1.25x + a

Since Johnny spent $43.75 and bought 25 tickets, we find a by replacing y with 43.75 and x with 25:

43.75 = 1.25×25 + a

Now solve for a

43.75 = 31.25 + a
43.75 - 31.25 = a
a = 12.50

Going back to the first equation:

y = 1.25x + 12.50


Part 2:
a) Let (9,8) be (x1,y1) and (4,-12) be (x2,y2)
The formula for slope is:

`m = (y2 - y1)/(x2 - x1) \\ m = ( - 12 - 8)/(4 - 9) \\ m = ( - 20)/( - 5) \\ m = 4`
b) For the point-slope equation, I'll use (9,8)
Using the formula:

`y - y1 = m(x - x1) \\ y - 8 = 4(x - 9)`
c) For the slope-intercept form, we solve for y in the point-slope formula:

`y - 8 = 4(x - 9) \\ y = 4x - 36 + 8 \\ y = 4x - 28`