Question

a roller skating rink offers a special rate for birthday parties. On the samr day, a party for 10 skaters cost $107 and a party for 15 skaters cost $137. How much would a party for 12 skaters cost?

Answer 1

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

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{137-107}{15-10}$

$m=\frac{30}{5}=6\ \frac{\ }{skater}$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=6\\point\ (10,107)$

substitute

$y-107=6(x-10)$

step 3

Convert to slope intercept form

$y-107=6x-60$

$y=6x-60+107$

$y=6x+47$

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

$y=6(12)+47$

$y=\ 119$