Question

Someone please help, 100 points.

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:
$m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 12 - 8}{4 - 9} \\ m = \frac{ - 20}{ - 5} \\ m = 4$
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:
$y - 8 = 4(x - 9) \\ y = 4x - 36 + 8 \\ y = 4x - 28$