Can the coaches use only one type of vehicle to transport the students?
B
b
Can you have a fraction of a car or van?
A
a
Graph:
Interpretation of the intercepts: See solution.
B
b
Example Solutions: (0,8), (12,0), (3,6), and (9,2)
Practice makes perfect
a
Let's start by considering the equation of the line that models the situation.
4x+6y=48
Note that the equation is written in standard form. To graph it, we will find the intercepts. Then we will plot and connect them using a straight edge. Let's start by finding the y-intercept. To do so, we will substitute 0 for x in the given equation.
The x-intercept is at the point (12,0). We can now plot these points to draw the graph of the function. Note that the x- and y-variables represent number of vehicles. Therefore, they cannot take negative values and our graph will be restricted to the first quadrant.
We are told that x represents the number of cars and y represents the number of vans being used to transport students. Therefore, the intercepts tell us that we can transport all 48 students using only one type of vehicle.
Intercept
Point
Interpretation
x-intercept
(12,0)
12 cars and 0 vans can be used to transport the students
y-intercept
(0,8)
0 cars and 8 vans can be used to transport the students
b
To find four different possible solutions, we need to find ordered pairs that lie on the graph and whose coordinates consist of integer values. We cannot use a fraction of a car or van. Luckily, we already found two solutions, the intercepts.
(0,8) and (12,0)
To find our last two pairs, let's look at the graph to identify potential points. Then we can check to make sure they do, in fact, satisfy the equation.
Looking at the graph, the points (3,6) and (9,2) appear to lie on the graph. Let's check!
Point
4x+6y=48
Simplified
( 3, 6)
4( 3)+6( 6)? =48
48=48 ✓
( 9, 2)
4( 9)+6( 2)? =48
48=48 ✓
Both points satisfy the equation. Let's write our four solutions and their interpretation.
ccc
Point & & Interpretation [0.8em]
(0,8) & & The students can be transported
& & using0 cars and 8 vans [0.8em]
(12,0) & & The students can be transported
& & using12 cars and 0 vans [0.8em]
(3,6) & & The students can be transported
& & using3 cars and 6 vans [0.8em]
(9,2) & & The students can be transported
& & using9 cars and 2 vans
