Question

Amina opens a savings account. She starts her savings account with 20 dollars she got as a gift for her birthday. Each week she adds 15 dollars to her account. This graph represents the amount in the account, y, after x weeks.
What is the slope of the line? Keep in mind, slope is the change in vertical distance for a given change in horizontal distance, or
vertical distance
horizontal distance
. You can use the points below to help you find the change in horizontal and vertical distance from one point to the other.
x
y
(3, 65)(4, 80)
0
1
2
3
4
5
6
7
8
9
10
11
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Number of weeks
Account balance (dollars)
Slope =

Answer 1

To find the slope of the line represented in the graph, we use the formula for slope:

\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the points (3, 65) and (4, 80):

- \(x_1 = 3\), \(y_1 = 65\)
- \(x_2 = 4\), \(y_2 = 80\)

Now we can calculate the change in \(y\) and \(x\):

\[
\text{change in } y = y_2 - y_1 = 80 - 65 = 15
\]
\[
\text{change in } x = x_2 - x_1 = 4 - 3 = 1
\]

Now substituting these values into the slope formula:

\[
\text{slope} = \frac{15}{1} = 15
\]

So, the slope of the line is

\[
\boxed{15}
\]

This means that for each week (each unit increase in \(x\)), Amina's savings increase by 15 dollars.