cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven
The city of Charolotte, NC charges $2.50 fee and $2.50 per mile for each cab ride
Write an equation in slope-intercept form to represent the amount charged, C, for m number of miles by the company in Charlotte.
The equation in slope-intercept form to represent the amount charged, C, for m number of miles by the company in Charlotte is:
C = 2.50m + 2.50
Write an equation in point-slope form to represent the amount charged, C, for m number of miles by the company in Charlotte. (Hint: Go to Desmos and convert the equation you created in #1 to a table. Use a point from the table)
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1 point
To write the equation in point-slope form, we need to find a point on the line.
Using the given information, we can calculate the amount charged for 1 mile:
C = 2.50(1) + 2.50
C = 2.50 + 2.50
C = 5
So, the point (1, 5) lies on the line.
The point-slope form of a linear equation is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Using the point (1, 5) and the slope 2.50, we can write the equation as:
C - 5 = 2.50(m - 1)
C - 5 = 2.50m - 2.50
C = 2.50m + 2.50
Write an equation in standard form to represent the amount charged, C, for m number of miles by the company in Charlotte. (Remember A cannot be negative and no fractions or decimals for any of the values)
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1 point
To write the equation in standard form, we need to eliminate any fractions or decimals and ensure that the coefficient of the x-term is positive.
The equation in slope-intercept form is:
C = 2.50m + 2.50
To eliminate the decimal, we can multiply the entire equation by 100:
100C = 250m + 250
Now, let's rearrange the terms to be in the standard form (Ax + By = C), where A, B, and C are integers:
-250m + 100C = -250
To make the coefficient of m positive, we can multiply the entire equation by -1:
250m - 100C = 250
Therefore, the equation in standard form is:
250m - 100C = 250
What does the y-intercept mean in the context of this problem? Hint: What do you pay when you step into the cab?
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1 point
In the context of this problem, the y-intercept represents the amount you pay when you step into the cab, even if you don't travel any distance (miles).
In this case, the y-intercept is the value of 2.50 in the equation C = 2.50m + 2.50.
So, when you step into the cab (when m = 0), you would be charged $2.50 as the base fee, regardless of the number of miles traveled.