Now, solve for the value of b, or the vertical intercept.

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

120
=
10·4+b

Answer 1

To find the value of \( b \), the vertical intercept in the equation \( y = 10x + b \), we can plug in one of the data points given. Let's use the point \( (4, 120) \).

Using the formula:

\[ y = 10x + b \]

Substituting \( x = 4 \) and \( y = 120 \):

\[ 120 = 10 \cdot 4 + b \]

Now simplify:

\[ 120 = 40 + b \]

To isolate \( b \), we subtract 40 from both sides:

\[ b = 120 - 40 \]

\[ b = 80 \]

Thus, the vertical intercept \( b \) is \( 80 \).