Question

Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points) Part B: Write the equation for the line of best fit in slope-intercept form and use it to predict the number of games that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)

Answer 1

A. The approximate y intercept appears to be about 1.8 (slightly less than 2). What this tells us is that someone with 0 months of practice could expect to win around 1.8 games.

B. Using slope intercept form and assuming that the y intercept is at (0, 1.8), the equation can be solved for by finding the slope first and then putting the slope and the y intercept into the equation.

Slope (m):
points (0, 1.8) and (1, 3.0)
(Y2-y1)/(x2-x1)=(3.0-1.8)/(1-0)=1.2/1=1.2

Equation:
Y=mx+b
Y=1.2x+1.8

Answer 2

Answer with explanation:

PART A:

We know that the y-intercept of a line is the y-value of the point where the x-value is zero i.e. it the place where it intersects y-axis.

Based on the graph we see that  the line of best fit intersects the y-axis very close to 1.8.

Hence, the approximate y-intercept of the line of best fit is: 1.8

It represents that 1.8 baseball games were won when they did not do any practice i.e. initially.

PART B:

We know that the slope-intercept form of a line is given by:

                  $y=mx+b$

where m is the slope of the line and b is the y-intercept of the line.

The y-intercept here is: 1.8

The line of best fit passes through (0,1.8) and (6,13)

Hence, the slope is:

$m=\dfrac{13-1.8}{6-0}\\\\\\m=1.8667$

   Hence, the slope intercept form is:

             $y=1.8667x+1.8$

Now we are asked to find the value of y when x= 13

i.e.

$y=1.8667\times 13+1.8\\\\y=26.0671$

which is approximately equal to 26 games.