We want draw a line to show the relationship between the number of hours the tent is rented x and the total cost of the tent y. To do so, we will find two points that lie on the line and connect them one at a time.
Finding the First Point
Note that the cost of the tent includes an additional $ 100 set-up fee. This fee does not depend on the number of hours the tent is rented. Therefore, if we rent the tent for 0 hours we will pay $ 100. This means that the line crosses the y-axis at the point (0,100). Let's mark this point on a coordinate plane!
Finding the Second Point
To get the second point we will find the slope of the line. Recall that the definition of the slope of a line can be written in terms of rise and run.
m=rise/run
In this case the cost of the tent is $ 500 per hour plus an additional fee. Therefore, the rise, or change in y, is 500 and the run, or change in x, is 1. We can substitute these values into the formula for the slope to calculate m.
m=500/1= 500
The value of the slope will be helpful to find another point on the line. When we move right 1 and then move up 500 from the point (0,100), we will obtain the second point (1,600).
Graphing the Line
Finally, we can connect the two points to obtain the line.
We want to find the equation of the line we drew in Part A. The desired equation has to follow a specific format.
y= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. Note that in Part A we found that the slope is 500. In addition, in Part A we noticed that the line crosses the y-axis at the point (0, 100). Therefore, the y-intercept is 100. Now that we have the slope and the y-intercept we can write our equation.
y= 500x+ 100
