Answer:
$119
Step-by-step explanation:
Let
x -----> the number of skaters
y -----> the cost for birthday parties
we have the points
(10,107) and (15,137)
step 1
Find the slope of the linear equation
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{137-107}{15-10}[/tex]
[tex]m=\frac{30}{5}=6\ \frac{\$}{skater}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=6\\point\ (10,107)[/tex]
substitute
[tex]y-107=6(x-10)[/tex]
step 3
Convert to slope intercept form
[tex]y-107=6x-60[/tex]
[tex]y=6x-60+107[/tex]
[tex]y=6x+47[/tex]
step 4
How much would a party for 12 skaters cost?
For x=12 skaters
substitute the value of x in the equation and solve for y
[tex]y=6(12)+47[/tex]
[tex]y=\$119[/tex]
