When two quantities x and y are proportional, the relationship can be represented by the equation y=mx.
B
The slope is a ratio of the vertical change to the horizontal change between two points.
C
Use the equation obtained in Part A.
A
y=9x
B
The cost of renting a kayak is 9 dollars per hour.
C
45 dollars. See solution.
Practice makes perfect
We know that the cost y in dollars to rent a kayak is proportional to the number x of hours that we need to rent the kayak. We want to write an equation that represents this situation. To do so, remember that when two quantities are proportional, the relationship can be represented by the following equation.
y=mx
Here, m is the constant of proportionality. Since it costs 27 dollars to rent the kayak for 3 hours, we can find the value of m for our case by substituting y= 27 and x= 3 into the above equation.
27=m( 3)
Now, let's solve this equation for m to find the constant of proportionality.
Let's graph the linear equation obtained in Part A by using a table of values. We will replace x with 2, 4, and 6 to find the value of y.
x
y=9x
y
2
y=9( 2)
18
4
y=9( 4)
36
6
y=9( 6)
54
The value of x and its corresponding value of y represents an ordered pair that can be plotted in a coordinate plane. Let's plot the ordered pairs and draw a line through the points.
Remember that the slope is a ratio of the vertical change to the horizontal change between two points.
m= Change iny/Change in x
In our case, y represents the cost to rent a kayak and x represents the hours that we need to rent the kayak. The slope will tells us the cost of renting per hour.
From the graph, we can see that the change in y is equal to 9 and the change in x is 1.
m= 9/1
Therefore, the cost of renting a kayak per hour is equal to 9 dollars.
We want to find the cost of renting a kayak for 5 hours. To do so, let's recall the equation obtained in Part A.
y=9x
We will substitute x= 5 into the above equation to find the cost of renting the kayak.
