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

Answer:

B. $y=\dfrac{9}{2}x+5$

Step-by-step explanation:

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

$y=mx+b.$

First, find the slope of the line:

$m=\dfrac{23-14}{4-2}=\dfrac{9}{2}$

Now, find the y-intecept b:

$y=\dfrac{9}{2}x+b\\ \\14=\dfrac{9}{2}\cdot 2+b\\ \\14=9+b\\ \\b=14-9\\ \\b=5$

Hence, the equaiton is

$y=\dfrac{9}{2}x+5$

Check all points:

$(2,14):\ \ \dfrac{9}{2}\cdot 2+5=9+5=14\\ \\(4,23):\ \ \dfrac{9}{2}\cdot 4+5=18+5=23\\ \\(6,32):\ \ \dfrac{9}{2}\cdot 6+5=27+5=32\\ \\(8,41):\ \ \dfrac{9}{2}\cdot 8+5=36+5=41$