Answer :
Answer:
[tex]2c=m+19[/tex]
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 : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(5,12)[/tex]
[tex](x_2,y_2)=(9,14)[/tex]
Substitute the values in the formula :
[tex]y-12=\frac{14-12}{9-5}(x-5)[/tex]
[tex]y-12=\frac{2}{4}(x-5)[/tex]
[tex]y-12=\frac{1}{2}(x-5)[/tex]
[tex]2y-24=x-5[/tex]
[tex]2y=x+19[/tex]
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: [tex]2c=m+19[/tex]
Hence an equation can be used to find the cost, c, for any distance, m, traveled is [tex]2c=m+19[/tex]