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Question 1110250: Problem: When the Jenkins family moved into their home 10 years ago, there were two small trees in their backyard. Both trees have since been growing at a constant rate. For the first tree, 6 years after the Jenkins moved in, it was 11 feet tall, and 8 years after they moved in, it was 13 feet tall. For the second tree, 7 years after the Jenkins moved in, it was 15 feet tall, and 9 years after they moved in, it was 19 feet tall.
Question 1: Derive equations for the first tree and the second tree, where x is the number of years since the Jenkins moved in and y is the height of the tree in feet.
Question 2: Graph both equations on a coordinate grid. (what are the coordinates?)
Question 3: From the graph, determine how many years after the Jenkins moved in that the first tree and the second tree were the same height, and give the height. Explain how you got your answer.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! When the Jenkins family moved into their home 10 years ago, there were two small trees in their backyard. Both trees have since been growing at a constant rate.
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Question 1: Derive equations for the first tree and the second tree, where x is the number of years since the Jenkins moved in and y is the height of the tree in feet.
"For the first tree, 6 years after the Jenkins moved in, it was 11 feet tall, and 8 years after they moved in, it was 13 feet tall."
x1=6, y1=11; x2=8, y2=13
find the slope; m =  =  = 1 is the slope
y - 11 = 1(x-6)
y = x - 6 + 11
y = x + 5 is the first equation, red
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For the second tree, 7 years after the Jenkins moved in, it was 15 feet tall, and 9 years after they moved in, it was 19 feet tall.
x1=7, y1=15; x2=9, y2= 19
find the slope m =  =  = 2 is the slope
y - 15 = 2(x-7)
y - 15 = 2x - 14
y = 2x - 14 + 15
y = 2x + 1, is the 2nd equation, green
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Question 2: Graph both equations on a coordinate grid. (what are the coordinates?)
Graph the two above equations
Question 3: From the graph, determine how many years after the Jenkins moved in that the first tree and the second tree were the same height, and give the height. Explain how you got your answer.
when the graphs intersect; x=4; y=9, 4 years after they move in the trees are the same height, 9 ft
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