a Determine from the graph where the function intersects with the axes.
B
bDomain is read from the x-axes, while range is read from the y-axis.
C
c Find the intersection of the function and the line x=12.
A
a -5/4
B
bDomain: x∈[0,24] Range: y∈[0,30]
C
c $1,500
Practice makes perfect
a We are asked to calculate the slope of the function shown on the graph below.
We can see that the function intersects the axes at (0,30) and (24,0). Using these points and the Slope Formula, we get the slope of the function.
m=y_2-y_1/x_2-x_1
Let's substitute the points into the formula.
Slope is equal to - 54, which means that every month your loan balance decreases by $125.
b We are asked to determine the domain and the range of the function.
We read the domain from the x-axis. The loan starts at x=0 and ends at x=24, so the domain is x∈[0,24]. That means it takes you 24 months to pay off the loan.
The range is read from the y-axis. At the beginning when you secure the loan, y=30. After 24 months you finally pay off the loan and y=0, so the range is y∈[0,30].
c In order to determine how much is owed after 12 months, we have to find the point of intersection of the function and the vertical line x=12.
We can see that the lines intersect at (12,15), which means that after 12 months you still owe $1500.
