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

$119

Explanation:

Answer 2

$119

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=(y2-y1)/(x2-x1)`

substitute the values

`m=(137-107)/(15-10)`

`m=(30)/(5)=6\ (\$)/(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`