The given table shows the balance of a student's bank account at various times.
Weekly Account Balance
Week
1
3
4
7
9
Account Balance
$35
$68
$85
$105
$136
To estimate the amount in Week 6, we need to write an equation to relate time and account balance. Let's start with making a scatter plot. First, plot the given data on the coordinate plane. Let the x-axis represent weeks and the y-axis represent the account balance.
Next, draw a trend line along the plotted points. Since this is an approximation, various lines for the data points can be drawn.
Now we will write the equation for the trend line. To do that, choose two points that lie on the line. As we can see, the points (1,35) and (9,136) appear to be on the line. We will write the equation in slope-intercept form.
y= mx+ b
In this form m is the slope and b is the y-intercept. First, we determine the slope by using the Slope Formula.
We have found that the slope is 12.6.
y=12.6x+ b
Now we will determine the y-intercept by substituting one of the points on the line into the equation. Any point on the trend line will satisfy this requirement, so let's use (1,35).
With the y-intercept we can write one possible equation for the line of fit.
y=12.6x+22.4
Last, we can estimate the amount of money in the account in Week 6 by substituting 6 for x into the equation.
