Consider that a costumer pays an initial fee and a daily fee to rent a snowmobile. We want to find the daily fee if the total payment for 3 days is 92 dollars and 120 dollars for 5 days. To do so, let's construct a table of values with this information where y represents the total payment in dollars and x represents the days.
x
y
3
92
5
120
The value of x and its corresponding value of y indicates an ordered pair that can be plotted in a coordinate plane. Let's plot the ordered pairs and draw a line through the points.
The slope of the line is a ratio used to compare how a variable changes in relation to another variable. We can calculate it by using the slope formula.
m = y_2-y_1/x_2-x_1
In our case, the slope will tell us the ratio between the total payment and the number of days. Let's substitute x_1= 3, y_1= 92, x_2= 5, and y_2= 120 into the Slope Formula.
Since the initial fee is the same for both cases, the difference between the payments will be the sum of the fees. If we divide this quantity by the difference between the days, we will obtain the daily fee.
Daily Fee=120-92/5-3
Let's calculate this to obtain the value of the daily fee.
Therefore, the daily fee is equal to 14 dollars. Note that the expression for the daily fee has the same form as the slope of the line obtained previously.
