Each year, the height of the tree increases at a constant rate. So, we can draw a line through these two points to show the linear relationship between the number of years and the height of the tree. Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line?

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= mx + b

Slope =

Answer 1

To find the slope \( m \) of the line that represents the relationship between the number of years \( x \) and the height of the tree \( y \), we can use the formula for slope:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the given points \( (4, 120) \) and \( (7, 150) \):

• Let \( (x_1, y_1) = (4, 120) \)
• Let \( (x_2, y_2) = (7, 150) \)

Now we can substitute these values into the slope formula:

\[ m = \frac{150 - 120}{7 - 4} \]

Calculating the differences:

\[ m = \frac{30}{3} = 10 \]

So, the slope \( m \) is \( 10 \).

To summarize, the slope of the line is:

\[ \text{Slope} = 10 \]