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

Answer 1

Slope = (16 − 7)/(9 − 6) = 9/3 = 3, so y = 3x + b. Using (6,7): 7 = 18 + b ⇒ b = −11, hence y = 3x − 11.

Thus the correct equations are:
- y − 16 = 3(x − 9) (point–slope at (9,16), expands to y = 3x − 11)
- y = 3x − 11

y − 6 = 3(x − 10) expands to y = 3x − 24 (wrong) and y = −3x − 23 is also wrong.