Find the equations of the lines. To find where they intersect, extend the coordinate plane.
System of Equations:b=2.5t+40 b=5t Same balance: 16 weeks
Practice makes perfect
To write the system of equations we have to determine the equations of both lines. To do so, we need the y-intercept and slope of each graph. Looking at the graphs, we can identify the y-intercepts as (0,0) and (0, 40).
Also, notice how the graph of Account 1 passes through the point (4,50) and the graph that describes Account 2 passes through the point (4,20). With this information, we can determine the rate of change for each graph.
Now we can find the rate of change by dividing the rise over run between the known points, RiseRun. Notice that this is the same thing as the slope of a graph.
Account1:& Slope=Rise/Run =10/4= 2.5 [0.8em]
Account 2:& Slope=Rise/Run =20/4= 5
Now we can write our system of equations.
b= 2.5t+ 40 b= 5t
To find when the accounts will have the same balance we have to determine the point at which the lines intersect. Since we cannot see this point on the given graph, we have to extend the coordinate plane.
The graphs intersect at the point (16,80). This means that after 16 weeks the balance in both bank accounts will the same.
Checking Our Answer
Finally we can check our answer by substituting 16 for t and 80 for b in our system of equations.
