Stephanie uses a ride service to get to different places in her city. If Stephanie uses Uber the service charges 1.50 per mile . If Stephanie uses lift the service charges $2.00 per mile. Let m represent the number of miles traveled. Which of the following statements are true . Select all that apply

By a small online search, i found that the actual question seems to be:

"Stephanie uses a ride service to get to different places in her city. If Stephanie uses Uber the service charges $5.00 plus 1.50 per mile . If Stephanie uses lift the service charges $2.00 per mile. Let m represent the number of miles traveled. Which of the following statements are true . Select all that apply"

The statements are not provided, so i will answer it in a general way.

We have two different equations:

1) a fixed amount of $5.00 plus $1.50 for each mile, m.

This is a linear equation:

y1 = $1.50*m + $5.00

2) No fixed amount, only $2.00 for each mile, m.

y2 = $2.00*m

Now, the things we can see are which service will be cheaper as a function of m.

To see this, we can see the difference between y1 and y2.

When the difference is negative, this means that y1 is cheaper.

When the difference is positive this means that y2 is cheaper.

When the difference is zero, both services charge the same.

D = y1 - y2 = $1.50*m + $5.00 - $2.00*m

                 = (-$0.50)*m + $5.00

First let's find when it is zero.

              0 =  (-$0.50)*m + $5.00

            5.00/0.5 = m = 10

So for 10 miles, both services charge the same.

As the coefficient that multipies m is negative, if we have m > 10, then the difference will be negative.

This means that for m > 10, y1 is cheaper.

Then for m < 10, y2 is cheaper.

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