Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven
the city of charlotte, NC charges $1.95 fee and $2.70 per mile for each cab ride.
6. For the Raleigh company, create a table to represent the cost of the cab ride given the number of miles provided for miles 5, 10, 15 and 20. List the cost for the cab ride for 15 miles.
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To write an equation in slope-intercept form to represent the amount charged for m number of miles, let's assume the equation is: C = mx + b.
In this case, the slope (m) represents the rate per mile, which is $2.70, and the y-intercept (b) represents the flat fee, which is $1.95.
Therefore, the equation in slope-intercept form is: C = 2.70m + 1.95.
To create a table representing the cost of the cab ride for the Raleigh company:
| Miles | Cost |
|-------|------|
| 5 |$1.95 + (5 * $2.70)|
| 10 |$1.95 + (10 * $2.70)|
| 15 |$1.95 + (15 * $2.70)|
| 20 |$1.95 + (20 * $2.70)|
To find the cost for the cab ride for 15 miles, substitute 15 into the formula:
Cost for 15 miles = $1.95 + (15 * $2.70) = $1.95 + $40.50 = $42.45
7. For the Raleigh company write an equation in slope-intercept form to represent the amount charged, C, for m number of miles.
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1 point
8. For the Raleigh company write an equation in point-slope form to represent the amount charged, C, for m number of miles for the company in Raleigh, NC.
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To write an equation in point-slope form to represent the amount charged for m number of miles, let's assume the equation is: C - C1 = m(m - m1), where (m1, C1) is a point on the line.
In this case, let's consider the point (0,1.95), where the flat fee is $1.95.
Therefore, the equation in point-slope form is: C - 1.95 = 2.70(m - 0) or C - 1.95 = 2.70m.
Simplifying the equation, we get: C = 2.70m + 1.95.
9. Write an equation in standard form to represent the amount charged, C, for m number of miles for the company in Raleigh.
To write an equation in standard form to represent the amount charged for m number of miles, we can rearrange the equation in point-slope form: C = 2.70m + 1.95.
To convert it to standard form, we can bring all the terms to one side of the equation:
-2.70m + C = 1.95.
Now, to eliminate the decimal, we can multiply both sides of the equation by 100:
-270m + 100C = 195.
Finally, in standard form, the equation that represents the amount charged for m number of miles for the company in Raleigh is:
270m - 100C = -195.
10. What does the slope mean in the context of the problem?
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