Question

The cost of a taxi ride is a linear function of the distance traveled. 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?

Answer 1

A linear function takes the form of:

y = mx + c

Where y is the dependent variable and x is the independent variable
m and c are constants. 

In this case, we will put c (cost) = y, and m (distance) = x

So,

c = kx + p  (Where k and p are constants that we need to determine)

If a 5-mile ride costs $12 and a 9-mile ride costs $14, 

⇒ 12 = 5m + p  ........ (i) and

14 = 9k + p .......... (ii)


Subtract (ii) from (i)

-2 = -4m

⇒ m = 0.5

Substitute in (i)

⇒ 12 = 5(0.5) + p

⇒ p = 9.5


And the equation becomes:

c = 0.5m + 9.5

Answer 2

Answer:

Step-by-step explanation:

A linear function takes the form of:

y = mx + c

Where y is the dependent variable and x is the independent variable

m and c are constants.

In this case, we will put c (cost) = y, and m (distance) = x

So,

c = kx + p (Where k and p are constants that we need to determine)

If a 5-mile ride costs $12 and a 9-mile ride costs $14,

⇒ 12 = 5m + p ........ (i) and

14 = 9k + p .......... (ii)

Subtract (ii) from (i)

-2 = -4m

⇒ m = 0.5

Substitute in (i)

⇒ 12 = 5(0.5) + p

⇒ p = 9.5

And the equation becomes:

c = 0.5m + 9.5