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
[tex] m=\frac{y2 - y1}{x2 - x1} [/tex] substitute and solve
m = [tex] \frac{15 - 3.75}{7.5 - 0} [/tex]
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.
