Question

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.
y - 6 = 3(x – 10)
y- 16 = 3(x-9)
y = 3x - 11
y=-3x-23
D
DONE

Answer 1

- (b) y -16 = 3(x -9)
- (c) y = 3x -11

Step-by-step explanation:

You are given a couple of points:

(years, heigh) = (6, 7) and (9, 16)

and asked to write a linear equation that they satisfy. In general, you need to find the slope using the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (16 -7)/(9 -6) = 9/3 = 3

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point-slope equation

The point-slope form of the equation for a line can be used with this information.

y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Using the given points, you can write either of the equations ...

y -7 = 3(x -6) . . . . . using the first point

y -16 = 3(x -9) . . . . . using the second point. This matches choice B.

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slope-intercept equation

Either of the point-slope equations can be rearranged to give the slope-intercept equation.

y -16 = 3(x -9)

y = 3x -27 +16 . . . . eliminate parentheses, add 16

y = 3x -11 . . . . . This matches choice C.

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Additional comment

The first choice has the right slope, but uses a point not on the line (10, 6).

The last choice has the wrong slope and the wrong y-intercept.