Let’s finish writing our equation to represent the relationship between the number of years and the height of the tree. Now that we know the value of b, or the vertical intercept, substitute the vertical intercept for b in our equation

Question

x
y
(4, 120)(7, 150)
0
1
2
3
4
5
6
7
8
9
10
0
15
30
45
60
75
90
105
120
135
150
165
180
Number of years
Height (inches)
y
=
10x + b
y
=
10x +
b
=
80

Answer 1

To complete the equation that represents the relationship between the number of years (x) and the height of the tree (y), you have provided the formula \( y = 10x + b \) and indicated that \( b = 80 \).

Substituting \( b \) into the equation:

\[ y = 10x + 80 \]

This linear equation suggests that for every year the tree grows (as represented by \( x \)), the height of the tree (as represented by \( y \)) increases by 10 inches, starting from a height of 80 inches when \( x = 0 \) (the intercept).

So your final equation representing the relationship between the number of years and the height of the tree is:

\[ y = 10x + 80 \]