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Your friend is trying to grow her hair as long as her cousin's hair. The table (attached) shows their hair lengths (in inches) in different months.
a. Write a system of linear equations that represents this situation.
b. Will your friend's hair ever be as long as her cousin's? If so, in what month?

Your friend is trying to grow her hair as long as her cousins hair The table attached shows their hair lengths in inches in different months a Write a system of class=

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clarch19

Answer:

a)  y = 1/2x + 5/2

    y = 2/5x + 29/5

b)  hair will be 19 inches for both at 33 months

Step-by-step explanation:

a) rate of growth of friend's hair:  (3, 4) (8, 6.5)  

(6.5 - 4) ÷ (8 - 3) = 2.5/5 or 1/2

find the y-intercept of equation for growth of friend's hair:

y = mx + b

4 = 1/2(3) + b

4 = 3/2 + b

8/2 - 3/2 = b

5/2 = b

equation for growth of friend's hair:

y = 1/2x + 5/2

rate of growth of cousin's hair:  (3, 7) (8, 9)  

(9 - 7) ÷ (8 - 3) = 2/5

find the y-intercept of equation for growth of cousin's hair:

y = mx + b

9 = 2/5(8) + b

9 = 16/5 + b

45/5 - 16/5 = b

29/5 = b

equation for growth of cousin's hair:

y = 2/5x + 29/5

b) y = 1/2x + 5/2

   y = 2/5x + 29/5

1/2x + 5/2 = 2/5x + 29/5

5/10x + 25/10 = 4/10x + 58/10

1/10x = 33/10

10x = 3300

x = 33

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