Question

use the number line below, where rs = 6y + 2, st = 4y + 9, and rt = 91.
a. what is the value of y?
b. find rs and st.

r s t

...

a. what is the value of y?
y = \boxed{} (type an integer or a decimal.)

Explanation:

Step1: Apply segment addition postulate

From the number line, \( RS + ST = RT \). Substitute \( RS = 6y + 2 \), \( ST = 4y + 9 \), and \( RT = 91 \) into the equation:
\( (6y + 2) + (4y + 9) = 91 \)

Step2: Combine like terms

Simplify the left - hand side:
\( 6y+4y + 2 + 9=91 \)
\( 10y+11 = 91 \)

Step3: Solve for y

Subtract 11 from both sides:
\( 10y+11 - 11=91 - 11 \)
\( 10y=80 \)

Divide both sides by 10:
\( y=\frac{80}{10}=8 \)

Answer:

\( y = 8 \)