Question

The graph below shows the relationship between the number of months different students practiced boxing and the number of matches they won.

Part A: what is the approximate y-intercept of the line of best fit and what does it represent?

Part B: write the equation for the line of best fit in the slope- intercept form and use it to predict the number of matches that could be won after 13 months of practice.


Show your work and explain your answer. Include the points used to calculate the slope

Answer 1

Short Answer:
Slope = 1.5
y = 1.5x + 3.75 <<<< Line.
Question A
The y intercept is between 3 and 4 1/2. Each square is worth 1.5 on the y axis. 1/2 of 1 square then is 0.75. So the y intercept in this case is 3.75 as a rough estimate.

The y intercept represents the number of victories a student can expect with absolutely no training whatever. It cannot go into the negative region. That would have no meaning at all in the outside world. There cannot be < 0 weeks of training when talking training training time.

Question B
The way to solve this part of the question is to use two well defined points.

One point would be (7.5, 15) and the other could be the y intercept since it is pretty clear. (0,3.75)

Step One
Find the slope
m = (y2 - y1) / (x2 - x1)

Givens
y1 = 15
y2 = 3.75
x1 = 7.5
x2 = 0

Formula

`m=(y2 - y1)/(x2 - x1)` substitute and solve

m =
`(15 - 3.75)/(7.5 - 0)`
m = 11.25 / 7.5 = 1.5

Note
We are finding the point associated with the line and not the closest raw data point.

So far what we have is
y = mx + b
y = 1.5x + b

Step Two
Find b.

We already have the y intercept, but we should confirm it with the other point. b = 3.75 from Problem A.

However
y = 15
x = 7.5

y = 1.5x + b
15 = 1.5*7.5 + b
15 = 11.25 + b Subtract 11.25 from both sides.
15 - 11.25 = b
b = 3.75 which is just the answer we got for problem A

Answer
y = 1.5x + 3.75 <<<<

If x = 13 then just put it in the equation above.
y = 1.5x + 3.75
y = 1.5*13 + 3.75
y = 23.25 victories. Since I don't know what your choices are, I would round down to 23.