The graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:
The title of the graph is Boxing Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 21 at increments of 3, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 3 and 1, 6 and 2, 7 and 3, 9 and 4, 11 and 5, 13 and 6, 14 and 7, 16 and 8, 17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 4 and 2, 7.1 and 4, 11 and 6, 13.5 and 8, 17 and 10, 20.5.
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)
Part A: The approximate y-intercept of the line of best fit is 4, and it represents the number of matches won by a student who has practiced boxing for 0 months.
Part B: To find the equation of the line of best fit, we first need to calculate the slope using two points on the line. Let's use the points (0, 4) and (6, 13), which gives a slope of:
Slope = (13 - 4) / (6 - 0) = 9 / 6 = 1.5
Now we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
y - 4 = 1.5(x - 0)
y = 1.5x + 4
Therefore, the equation for the line of best fit is y = 1.5x + 4.
To predict the number of matches that could be won after 13 months of practice, we substitute x = 13 into the equation:
y = 1.5(13) + 4
y = 19.5 + 4
y = 23.5
Therefore, the prediction is that a student who has practiced boxing for 13 months could win approximately 23.5 matches.