Answer:
\(2c=m+19\)
Step-by-step explanation:
Given : The cost of a taxi ride is a linear function of the distance traveled.
To Find: If a 5-mile ride costs $12 and a 9-mile ride costs $14, which equation can be used to find the cost, c, for any distance, m, traveled?
Solution:
The cost of a taxi ride is a linear function of the distance traveled.
We are given that a 5-mile ride costs $12 and a 9-mile ride costs $14
So, Points are (5,12) and ( 9,14)
Now to find an equation can be used to find the cost, c, for any distance, m, traveled
We will use two point slope form.
Formula : \(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)
\((x_1,y_1)=(5,12)\)
\((x_2,y_2)=(9,14)\)
Substitute the values in the formula :
\(y-12=\frac{14-12}{9-5}(x-5)\)
\(y-12=\frac{2}{4}(x-5)\)
\(y-12=\frac{1}{2}(x-5)\)
\(2y-24=x-5\)
\(2y=x+19\)
where x is the distance and y is the cost
Let us say m denotes the distance and c denotes the cost
So, equation becomes: \(2c=m+19\)
Hence an equation can be used to find the cost, c, for any distance, m, traveled is \(2c=m+19\)