Question

6. Volunteer drivers are needed to bring 80 students to the championshipbaseball game. Drivers either have cars, which can seat 4 students, orvans, which can seat 6 students. The equation 4C + 6 = 80 describes therelationship between the number of cars c and number of vans v that cantransport exactly 80 students.Explain how you know that this graphrepresents this equation. *

Answer 1

`4C+6V=80`

Let's make

v = Y

C= X

`4x+6y=80`

We are going to use x-intercept and y-intercept to check if the graph is correct

`\begin{gathered} 4x+6y=80 \\ \text{make y the subject } \\ 6y=80-4x \\ \text{divide both sides by 6} \\ y=(80-4x)/(6) \end{gathered}`

The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0

`\begin{gathered} y=(80-4x)/(6) \\ x=0 \\ y=(80-4(0))/(6) \\ \\ y=(80-0)/(6) \\ y=(80)/(6) \\ \\ y=13.33 \\ (0,13.33) \end{gathered}`

The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero

`\begin{gathered} y=(80-4x)/(6) \\ \\ \text{when y=0} \\ 0=(80-4x)/(6) \\ cross\text{ multiply} \\ 0*6=80-4x \\ 0=80-4x \\ 80=4x \\ \text{divide both sides by 4} \\ (80)/(4)=(4x)/(4) \\ \\ x=20 \\ (20,0) \end{gathered}`

Since, the x-intercept and y-intercept are correct the graph is true for the equation