Question

2. A 2-mi cab ride costs $5.25. a 5-mi cab ride costs $10.50. Which equation models the cost y of the cab ride for ride that is x miles?

A) Y = 1.75x – 1.75
B) Y = 1.75x + 1.75
C) Y = -1 1.75x – 1.75
D) Y = -1.75x + 1.75

Answer 1

By using the info above, I just substitute it into an equation. The answer should be B) y = 1.75x + 1.75 because 5.25 = 1.75(2) + 1.75, and 10.5 = 1.75(5) + 1.75. In other words, both of those fit into the equation.

Answer 2

Option B -
`y=1.75x+1.75`

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
`y=mx+b`

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

`m=(y_2-y_1)/(x_2-x_1)`

`m=(10.50 - 5.25)/(5 - 2)`

`m=(5.25)/(3)`

`m=1.75`

The equation form is
`y=1.75x+b`

Now, substitute x=2 and y=5.25 to find b

`5.25=1.75(2)+b`

`5.25=3.5+b`

`b=1.75`

Now, The required equation models the cost y of the cab ride for ride that is x miles is
`y=1.75x+1.75`

Therefore, Option B is correct.