We are asked to graph a system of equations that represent the total cost of renting a canoe as a function of thr number of rental hours
The first rental for river Y is $33 (fixed) for the rental
the second option is for river Z which consists of a fixed $13 fee, and on top of that $5 per hour.
Then we can write the following cost for river Y:
Y = 33 (independent of number of hours). So this is a constant horizontal line that goes through the point 33 on the vertical axis.
And for river Z we have the following equation which does change with the number of hours of the rental:
Z = 5 n + 13
(where n is the number of hours of rental) This expression is also a line, but with slope "5" .
Allow me a little time to plot the graph of the two lines and upload the image here.
The green horizontal line represents the cost of reanting the river Y trip, and the orange line represents the cost of renting the Z river trip .
Notice that to plot the orange line, we start at the point 13 in the vertical axis, because that corresponds to the $13 fixed fee one has to pay for the river X rental. then, as one hour goes by, from the 13 we have to jump to the value $13 + $5 = $18.
So notice that from the initial 13 in the vertical axis, as we go to the right in ONE unit (one hour), the new cost has now increased to $18 (see that the line goes through the point (1, 18) meaning after 1 hour, the cost is now $18. This process will repeat every time we move one step (tick mark/division) to the right. One step to the right (one more hour went by), we need to move the cost up in $5.
We can solve the system of these two equations by finding the point at which both lines intersect, since that would be the point at which both costs are the same.
We see that the lines intersect at the point (4, 33) which means 4 hours and $33. Then a 4 hour rental in river Z would cost the same as the fixed rental in river Y.