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Writing Two-Variable Linear Equations

Question 10 • 26/27 ALGEBRA II A

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 – 11y = –3x – 23

Answer
A
y – 6 = 3(x – 10)
B
y – 16 = 3(x – 9)
C
y = 3x – 11
D
y = –3x – 23

Explanation

The tree’s constant growth rate is (16 − 7) ÷ (9 − 6) = 3 feet per year. Using the point (9, 16), the equation is y − 16 = 3(x − 9), which is choice B. Expanding gives y = 3x − 11, which is choice C. Choice A uses a point that is not on this line, and choice D has the wrong slope.

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