# A 3-mile cab ride costs $3.00. A 6-Mile cab ride costs $4.80. How do you find a linear equation that models cost (c) as a function of distance (d)?

##### 2 Answers

#### Explanation:

The

For a

The cost of

Therefore the cost for

The basic fee for hiring the cab is

So the total cost,

Check:

If

If

Use

Plug this slope

#### Explanation:

Our goal is an equation of the form

The given data says that when our input (distance) is 3 miles, our output (cost) is $3.00. This gives us the data point

If our model is linear (which we are told it is), then these two points **must** be on the line. And two points is all we need to define a line, so these two points can help us write the equation for this linear model.

**Step 1:** Use

For any two points, the slope of the line between them is the ratio of "how far the points are from each other vertically" to "how far they are from each other horizontally". In other words, rise over run.

In this question, since cost is modeled as a function of distance, cost will be plotted along the vertical axis (rise), and distance will be along the horizontal axis (run).

#m=(c_2-c_1)/(d_2-d_1)= (4.8-3)/(6-3)#

#color(white)(m=(c_2-c_1)/(d_2-d_1))=(1.8)/(3)" "=0.6#

So for each extra mile we travel, the cost will go up by $0.60.

**Step 2:** Use

Knowing that the cost per mile is $0.60, we can use this with one of the given data points to find the base charge

#" "c_0" "=m(d_0)+b#

#" "3" "=0.6(3)+b#

#" "3" "=" "1.8" "+b#

#1.2=" "b#

So each cab ride starts with a base charge of $1.20.

**Step 3:** Place the known values for

We now have enough information to write a formula for the cost

#c=md+b#

becomes

#c=0.6d+1.2" "or" "c=$0.60d+$1.20#

In other words, the cost