Check it out!

Check it out!

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3.1.2: Intersecting Graphs

Brian is older than his brother Andrew by 2 years. Brian likes to remind Andrew that he is both older and taller and tells Andrew that it will always be this way. But one day their father overhears Brian and makes a prediction. “Andrew, your brother will always be older than you, but one day you will be taller—and I can prove it mathematically.”

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3.1.2: Intersecting Graphs

He writes two equations, one describing Brian’s growth rate, the other describing Andrew’s growth rate. Both equations are in terms of Brian’s age in years, x; the final value, y, is each boy’s height in feet. Assume that the boys will finish growing at age 20.

Use the equations to complete the problems.

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3.1.2: Intersecting Graphs

Brian’s growth rate: Andrew’s growth rate:

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3.1.2: Intersecting Graphs

1. Make a table of values for the two equations.

2. Graph the equations on the same coordinate plane.

3. According to the graph, will Andrew be taller than Brian?

4. If Andrew does outgrow Brian, how old will Andrew be when he does?

1. Make a table of values for the two equations.• List values for x, and then find the corresponding

values for y for each boy.

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3.1.2: Intersecting Graphs

x

0 2.25 not born yet

2 2.65 2

4 3.05 2.5

10 4.25 4

15 5.25 5.25

16 5.45 5.5

20 6.25 6.5

2. Graph the equations on the same coordinate plane.

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3.1.2: Intersecting Graphs

Hei

ght i

n fe

et

Brian’s age in years

3. According to the graph, will Andrew be taller than Brian?• Yes, Andrew will be taller.

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3.1.2: Intersecting Graphs

4. If Andrew does outgrow Brian, how old will Andrew be when he does?• Andrew will outgrow Brian shortly after Brian turns

15. Andrew is 2 years younger than Brian. Andrew will be 15 – 2 or 13 years old when he outgrows Brian.

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3.1.2: Intersecting Graphs