Question

Use the number line below, where RS = 6y + 2, ST = 2y + 7, and RT = 12y- 11.

a. What is the value of y?
b. Find RS, ST, and RT.

Answer 1

Therefore,

`y = 5`

`RS=32\\ST=17\\RT=49`

Explanation:

Given:

`RS = 6y+2`

`ST = 2y+7`, and

`RT = 12y- 11`

To Find:

`y = ?`

`RS=?\\ST=?\\RT=?`

Solution:

Consider a line R - S - T as shown below such that,

`RT=RS+ST` ............Line Addition Property

Substituting the values we get

`12y-11=6y+2+2y+7\\\\12y-8y=11+9\\\\4y=20\\\\\therefore y=(20)/(5)=5\\y=5`

Substituting the value 'y' we get

`RS=6* 5+2=32\\ST=2* 5+7=17\\RT=12* 5-11=49`

Therefore,

`y = 5`

`RS=32\\ST=17\\RT=49`