Question 1. Suppose 𝑓(𝑥) is a linear function that gives the cost (in dollars) of being driven 𝑥 miles by an Uber driver. Given that 2 miles costs $11, and 10 miles costs $35, determine the following:

a) Find a formula for 𝑓(𝑥).

b) Interpret the 𝑦-intercept of your formula in terms of the situation described above, including units in your answer.

c) Interpret the slope of your formula in terms of the situation described above, including units in your answer.

Question

Question 1. Suppose 𝑓(𝑥) is a linear function that gives the cost (in dollars) of being driven 𝑥 miles by an Uber driver. Given that 2 miles costs $11, and 10 miles costs $35, determine the following:

a) Find a formula for 𝑓(𝑥).

b) Interpret the 𝑦-intercept of your formula in terms of the situation described above, including units in your answer.

c) Interpret the slope of your formula in terms of the situation described above, including units in your answer.

zarkam21 · Answer

@dude @SmokeyBrown

SmokeyBrown · Answer

So, assuming the equation is linear, in order to find the slope we'll take the change in the dependent variable divided by the change in the independent variable.
In this case, the dependent variable is the cost, and independent variable is the distance.
So, the distance goes from 2 to 10 miles, so that's a difference of 8 miles.
The cost changes from $11 to $35, which is a difference of $24
That means that every 8 miles extra costs $24 extra. If we divide, we'll find that each 1 mile costs an additional $3.
If it costs $11 for 2 miles, it would cost $8 for 1 mile, and $5 for no miles. Thus, $5 would be the y-intercept. This represents the base fee for a ride, no matter the distance.

zarkam21 · Answer

okay so part a, find the formula : f(x)=3m+24?

zarkam21 · Answer

and part b is $5 is the y intercept because it represents the base fee for a ride no matter what the distance

zarkam21 · Answer

@dude

dude · Answer

Watch out, the equation of a line is y=mx+b where b is the y-intercept

f(x)=3m+24 
What you wrote says that 24 is the q-intercept which isnt true (off of SmokeyBrown)

dude · Answer

y-intercept*

zarkam21 · Answer

y intercept is 5 so f(x)=5x?

dude · Answer

$y=nx+b$ is the equation of the line
y and $f(x)$ are the same thing (you can use these interchangably)
$n$ = the hourly rate (which is 3)
$b$ = the flat fee/ how much you have to pay for the service

(You only have to change the b value)

$y=3x+\_$?
5 is the flat fee
So..
Your equation is $f(x)=3x+5$
You can change the variable to be anything

zarkam21 · Answer

so for part c it would be 11?

dude · Answer

No no
Part A is $f(x)=3x+5$ or $f(x)=3m+5$ (Your variable doesn't matter)

Part B is 5, and the y-intercept represents the Uber's flat fee, which is $5

Part C is 3, for every mile that you travel with the driver, the fare will go up 3 dollars