Problem 1
x = number of years
y = height of the tree in inches
The equation for the first tree (your teacher doesn't mention the type of it) is y = 5x+7.
The 5 represents the slope or rate of change. It tells us how fast the tree is growing per year. The 7 at the end is the y intercept, and the starting amount. Refer to y = mx+b form.
Similarly, the equation for the second tree (oak tree) is y = 3x+11 because it starts off at a y intercept of 11 inches and increases by 3 inches per year, aka the slope.
I recommend making a table of values to see how each tree grows throughout the years.
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Answer:
The two equations are
y = 5x+7
y = 3x+11
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Problem 2
Let's use substitution to solve for x and y
y = 3x+11
5x+7 = 3x+11 .... replace y with 5x+7
5x-3x = 11-7
2x = 4
x = 4/2
x = 2
Use this x value to find y
y = 3x+11
y = 3*2+11
y = 6+11
y = 17
Or you could say
y = 5x+7
y = 5*2+7
y = 10+7
y = 17
We get the same y value either way, which helps confirm the answer.
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Answer:
(x, y) = (2, 17)
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Problem 3
The result of the previous problem was (x, y) = (2, 17) which is a compact way of saying that x = 2 and y = 17 pair up together.
Going back to how we defined x and y, we can see that x = 2 means that 2 years have passed and y = 17 means that both trees are 17 inches tall.
Interpretation: At the 2 year mark, both trees are 17 inches tall.
Note: 17 inches = 12 in + 5 in = 1 ft + 5 in
