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? (5 points)

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 include the points used to calculate the slope. (5 points)

Answer 1

Answer: The answers are given below.

Step-by-step explanation: Given that the graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:.

Part A : We are to find the approximate y-intercept of the line of best fit and state what does it represent.

From the graph, we note that

at x = 0, the value of y is approximately 3.

So, the approximate y -intercept of the line of best fit is 3.

It represents that before starting the matches, the students can win 3 matches without any practice.

Part B : We are to 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.

From the graph, we note that the line of best fit passes through the points (2, 7) and (9, 18).

So, the slope of the line of best fit will be

`m=(18-7)/(9-2)=(11)/(7).`

Therefore, the slope-intercept form of the equation of the line of best fit is given by

`y=mx+c\\\\\Rightarrow y=(11)/(7)x+3.`

Thus, the number of matches that could be won after 13 months of practice is

`y=(11)/(7)*13+3=23.42.`

That is, students can win 23 matches with 13 months of practice.