Question

Company “A” can transport 56 people in one hour. Graph the amount of people that can be transported in 12hrs. Graph. Company “B” Can transport 360 people in one hour. Graph the amount of people that can be transported in 12hrs. Graph. Q: Between companies, what is the difference in total passengers transported within a 12 hour period?1. Write a linear equation of the form y1 = mx + b for your first set of data.2. Write a linear equation of the form y2 = mx + b for the other equation in your system. 3. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect.4. Explain the point of intersection.

Answer 1

1.

We know that the equation of a line with slope m and y-intersect b is written as:

`y=mx+b`

For company A we know that it can transport 56 people in one hour, if we let x be the number of hours and y the number of people the company transport then, the slope in this case will be 56. The y-intersect will be the amoun of people they can transport in zero hours and this has to be zero, hence b=0. Therefore, the equation for company A is:

`y=56x`

2.

For company B we know that it can transport 360 people in one hour, hence the slope in this case is 360. Similarly as before we expect the y-intersect to be zero. Therefore, the equation for company B is:

`y=360x`

3.

Now, to graph a line on the graph we need to points. For both equation we notice that, when x=0, then y=0; this means that both lines will pass through the origin. To determine a second point for each line we choose a value for x, in this case we will use x=12, then we have:

`\begin{gathered} \text{ Company A} \\ y=56(12) \\ y=672 \\ \text{ Company B} \\ y=360(12) \\ y=4320 \end{gathered}`

Then the first line passes through (12,672) and the second line passes thorugh (12,4320).

We plot the point on the plane and graph the lines, the graph is shown below:

4.

The intersection, as we said, is the origin. In this case the intersection of the lines is the amount of people each company can transport in zero hours.

Finally we answer the first question, from the points in the graph we have that the difference between total passangers transported within 12 hours is 3648 passangers.