Question

Can someone pls help me with this thx

Answer 1

The y-intercept in coordinate form is (0, 2.9), which the y-intercept represents the pickup fee which is $2.90 before any mileage

Explanation:

Hello, I do apologize that no one responded for two hours.

1 - Understanding what it means to be a y-intercept

When mathematics presents the "y-intercept" its the unimaginative way of saying "Where the equation crosses the y-axis"

Looking at a graph we can deduce that, the y axis in traditional graphs is always at the x value of 0.

What can this mean for this situation?

We want to find out how much each person with 0 miles or no miles driven.

This will be our pickup fee alone

How can we do this?

Theres multiple ways, however the way I like is to set an equation to zero.

2 - Slope Intercept Form

We need to get it into the slope-intercept form using data given to us to use as our equation.

For reference the slope-intercept form is

y = mx + b

y = y value

m = slope

x = x value

b = y - intercept

2.1 - Find the slope

for y = mx + b we'll need to find our slope, m, and to do so we use the following formula

`slope = m = (\triangle y)/(\triangle x) = (change~in~y)/(chnage~in~x) = (y_2 ~ - ~ y_1)/(x_2 ~ - ~ x_1)`

To do this we need to assign x values and y values.

Our total cost is our y value, because its a total, and our variable is x which will be our miles.

(x value is always the variable, and our y value is always the totals)

So now looking at the data;

Gus;

$12.00 for a 6.5-mile journey

Tony;

$15.50 for a 9-mile journey

We can deduce at 6.5 miles we'll pay $12, and at 9 miles we'll pay $15.50

Because 6.5 is less than 9 our x1 and y1 will be deduced from that, and with that in mind, let's solve that equation.

POINT → (x, y)

(6.5, 12)

(9, 15.50)

`(y_2 ~ - ~ y_1)/(x_2 ~ - ~ x_1) = (15.50 ~ - ~ 12.00)/(9 ~ - ~ 6.5) = (3.5)/(2.5) = 1.4`

Our slope is 7/5, so therefore,

y = mx + b

=

y = 1.4x + b

2.2 - Plug and chug to find our y-intercept, b.

We'll need to plug in a point into the unfinished equation to solve for b

y = 7/5x + b

In this instance let's use (6.5, 12)

(x, y)

12 = 1.4(6.5) + b

12 = 9.1 + b

-9.1 -9.1

2.9 = b

Lets plug that in to our y = mx + b

y = 1.4x + b

↓

y = 1.4x + 2.9

And would you look at that, just by setting up the equation we now know our y-intercept, now if you recall from earlier one of my notes said this:

POINT → (x, y)

This is the same thing as coordinate form I'm assuming, and as a result, we have all the information we need to answer the problem.

3 - Putting it together to answer the problem

POINT → (x, y)

=

Coordinate Form:

=

(x, y)

Now remembering what I said earlier, the y-axis, is always on x = 0

So our y-intercept in coordinate form is;

(0, 2.9)

This means;

The pickup fee is $2.90 which excludes any mileage.

See the answer for it put together

Hope this helps :)