Six years after a tree was planted, its height was 7 feet. Nine years after it was planted, its height was 16 feet. Which of the following equations gives the height y, in feet, of the tree after x years if the tree grows at a constant rate? Check all of the boxes that apply.

Question

Mathematics

Kailey Kane

26 January, 16:55

Six years after a tree was planted, its height was 7 feet. Nine years after it was planted, its height was 16 feet. Which of the following equations gives the height y, in feet, of the tree after x years if the tree grows at a constant rate? Check all of the boxes that apply.

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Answers (1)

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Regina Gentry · Answer 1

Considering that the grows at a constant rate we can form an equation where x = how many years after it was planted

and y = its height

Now we just need to find how many feet it grows each year. To do that we just need to compare its height from a certain age to another:

6 years after it was planted : 7 feet,

so x=6 and y = 7

9 years after it was planted: 16 feet

so x = 9 y=16

With thay we can conclude that in 3 years, the tree grew 9 feet. To discover how much the tree grow each year we just nee to divide 9 feet by 3 years which is 3 feet every year.

To write the equatopn now we just need to find the y-intercept which we can discover by setting x to 0:

If in 6 years after the tree was planted it is 7 feet long, we can discover how long it was when it was planted by subtracting 6 years of growth (The slope) which is 3

7 - 6 (years) * 3 (feet the tree grow each year)

7 - 18 = - 11

The tree was - 11 feet long when it was planted

which is our y-intercept

(I know it doesnt make sense, but if you apply to a graph it will make more sense)

Now we can make the equation

y = 3x - 11