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
Step-by-step 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
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)
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 :)
