Question

The table shows the height of a tree as it grows. What equation in slope-intercept form gives the height of the tree at any time?

A) y= 9x+5

B) y= 9/2x+5

C) y= 9/2x

D) y= 5x+9/2


Table:

Time | Height
(month) (inches)
2 | 14

4 | 23

6 | 32

8 | 41

Answer 1

B.
`y=(9)/(2)x+5`

Explanation:

The equation of the line in the slope-intercept form is

`y=mx+b.`

First, find the slope of the line:

`m=(23-14)/(4-2)=(9)/(2)`

Now, find the y-intecept b:

`y=(9)/(2)x+b\\ \\14=(9)/(2)\cdot 2+b\\ \\14=9+b\\ \\b=14-9\\ \\b=5`

Hence, the equaiton is

`y=(9)/(2)x+5`

Check all points:

`(2,14):\ \ (9)/(2)\cdot 2+5=9+5=14\\ \\(4,23):\ \ (9)/(2)\cdot 4+5=18+5=23\\ \\(6,32):\ \ (9)/(2)\cdot 6+5=27+5=32\\ \\(8,41):\ \ (9)/(2)\cdot 8+5=36+5=41`