# a. For the first company, express in words the amount the cab company charges per ride and per mile.

Charges per ride \$3.00 per mile \$0.50

b. Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did.

Don't know

How would I do b i already did a

## \$3 to get in the cab (zero miles)

... y-intercept

\$0.50 per mile
... slope

x-axis is the independent variable ... miles

y-axis is the dependent variable
... price is dependent on milage

b. cost = \$.50 (miles) + \$3

## \$3 to get in the cab (zero miles)

... y-intercept

\$0.50 per mile
... slope

x-axis is the independent variable ... miles

y-axis is the dependent variable
... price is dependent on milage

## What does the slope mean in the context of the problem?

Cabs use a valuable commodity—gas! Research average gas prices from 2005–
2015 for the city you chose.
a. Create a table showing the average gas price each year.
b. Create a scatter plot of the data in your table.
c. What equation models the data? What are the domain and range of
d. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither?
How much do you expect gas to cost in 2020? Explain.

## Well, if you already know the rate per ride and per mile, you can use that information to write an equation.

Let's say the total cost of a ride (y) is based on the number of miles (x) traveled. The company charges \$3.00 for each ride, regardless of the distance traveled, and an additional \$0.50 per mile.

We can express this in slope-intercept form:

y = mx + b

In this case, the slope (m) represents the cost per mile, which is \$0.50. The y-intercept (b) represents the starting cost of \$3.00.

Thus, the equation becomes:

y = 0.50x + 3.00

I chose slope-intercept form because it allows us to easily identify the cost per mile and the starting cost.

## To answer part b, you need to choose a form (slope-intercept, point-slope, or standard form) and write an equation for the given information. Let's go through each form and determine which one is most appropriate.

1. Slope-intercept form: y = mx + b
This form is typically used when you know the slope (m) and y-intercept (b) of a linear function. However, in this case, we don't have enough information to determine the slope or y-intercept. So, we can exclude this form.

2. Point-slope form: y - y₁ = m(x - x₁)
This form is used when you know the coordinates of a point (x₁, y₁) and the slope (m). Unfortunately, we don't have any specific points given in the problem, so we can't use this form either.

3. Standard form: Ax + By = C
This form is used when you have the coefficients A, B, and C, which can be any real numbers. In this case, we have the information about the charges per ride and per mile. We can express these charges as:

Charge per ride: \$3.00
Charge per mile: \$0.50

To write an equation, we can assign variables to represent the unknowns. Let's say x represents the number of miles and y represents the total amount charged. We can write the equation as:

y = \$3.00 + (\$0.50)x

This equation shows that the total amount charged (y) depends on the number of miles (x), where the base charge is \$3.00 and an additional \$0.50 is added for each mile.

Therefore, the equation we chose is in standard form because it allows us to represent the given information most accurately.