Answer:
Option B - [tex]y=1.75x+1.75[/tex]
Step-by-step explanation:
Given : A 2-mi cab ride costs $5.25. a 5-mi cab ride costs $10.50.
To find : Which equation models the cost y of the cab ride for ride that is x miles?
Solution :
Assuming the model of the cost of the cab is linear.
So, The general form of linear is [tex]y=mx+b[/tex]
where, m is the slope and b is the y-intercept.
x is the distance in miles and y is the cost of the cab.
According to question,
A 2-mi cab ride costs $5.25. a 5-mi cab ride costs $10.50.
i.e. two points of the line (2,5.25) and (5,10.50).
Now, we find the slope of the line
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{10.50 - 5.25}{5 - 2}[/tex]
[tex]m=\frac{5.25}{3}[/tex]
[tex]m=1.75[/tex]
The equation form is [tex]y=1.75x+b[/tex]
Now, substitute x=2 and y=5.25 to find b
[tex]5.25=1.75(2)+b[/tex]
[tex]5.25=3.5+b[/tex]
[tex]b=1.75[/tex]
Now, The required equation models the cost y of the cab ride for ride that is x miles is [tex]y=1.75x+1.75[/tex]
Therefore, Option B is correct.
