Question

Use the number line below, where RS = 9y + 3, ST = 2y + 9, and RT = 16y - 8.

a. What is the value of y?
b. Find RS, ST, and RT.
a) (y = 2)
b) (y = 3)
c) (y = 4)
d) (y = 5)

Answer 1

The value of y is determined to be 4. Substituting this value into the given number line equations, we find that the lengths of RS, ST, and RT are 39, 17, and 56, respectively.

Step-by-step explanation:

The question requires solving for y using the given number line equations: RS = 9y + 3, ST = 2y + 9, and RT = 16y - 8. To find the value of y, we can use the fact that the sum of RS and ST is equal to RT because they are segments on the same line:

RS + ST = RT
9y + 3 + 2y + 9 = 16y - 8

Combining like terms gives:
11y + 12 = 16y - 8

Subtracting 11y from both sides and adding 8 to both sides, we get:
20 = 5y

Dividing both sides by 5 yields:
y = 4

This gives us the value of y. With y determined, we can then calculate the lengths of RS, ST, and RT by substituting y = 4 into each equation:

RS = 9(4) + 3 = 36 + 3 = 39
ST = 2(4) + 9 = 8 + 9 = 17
RT = 16(4) - 8 = 64 - 8 = 56