Answer: Carlton's cabs is the cheaper option if she wants to travel 15 miles.
Explanation:
A linear relationship can be written as:
c = a*n + b
where a is the slope (in this case, the rate per mile), n is the number of miles driven by the taxi, and b is the y-axis (in this case, the initial cost) intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then for each table we only need to take two points and construct the linear equation:
Treveon's Taxis:
We can use the two points (1, $5.25) and (3, $9.75)
Then the rate per mile, or the slope, will be:
a = ($9.75 - $5.25)/(3 - 1) = $2.25
This means that each mile costs $2.25
Then the equation will be written as:
c = $2.25*n + b
To find the value of b, we can just replace one of the points in the equation. For example, I will se the point (1, $5.25) this means that we need to replace n by 1, and c by $5.25
Then:
$5.25 = $2.25*1 + b
$5.25 - $2.25 = b
$3 = b
Then the initial cost here is $3.
And the equation will be:
c = $2.25*n + $3.
Carlton's Cabs:
Same approach as before, here I will use the points (1, $7.00) and (3, $10.50)
Then the rate per mile will be:
a = ($10.50 - $7.00)/(3 - 1) = $1.75
The rate per mile is $1.75 (is cheaper than in the previous case)
Then at the moment, the equation is:
c = $1.75*n + b
To find the initial cost, we do the same as before, here i will use the point (1, $7.00)
$7.00 = $1.75*1 + b
$7.00 - $1.75 = b
$5.25 = b
The initial cost here is $5.25
And the equation will be:
c = $1.75*n + $5.25
Now, which one is cheaper for 15 miles?
We only need to replace n by 15 in both equations, and see in which one the cost is lower:
Treveon's Taxis:
c(15) = $2.25*15 + $3 = $36.75
Carlton's Cabs:
c(15) = $1.75*15 + $5.25 = $31.5
Then Carlton's Cabs is a better option if you want to travel 15 miles.