We are given a table that shows the numbers of days spent training and the race times for several people in a race. With this data, we want to make a scatter plot and draw a line of fit. Let's start by considering the given table.
A line of fit is a line drawn on a scatter plot that is close to most of the data points. It can be used to estimate data on a graph. Keep in mind that this line does not actually need to pass through any of the data points.
Let's now find the equation of our line. To do so, we will need to use two points that fall on the line. It is always easier to choose points that belong to the given data set.
We can use the points (7,23.85) and (14,22.30).
The slope of the line is - 0.22. With this information, we can write its partial equation in slope-intercept form.
y= - 0.22x+b
To find the y-intercept b, we will use the fact that the line passes through the point (7,23.85). We will substitute 7 for x and 23.85 for y, then solve for b.
The y-intercept of the line is 25.39. We have all the information we need to write the equation of the line!
y=- 0.22x+ 25.39
Let's consider the equation we obtained in Part B. Recall that in our case x represents the days spent training and y represents the race time.
y= - 0.22x+ 25.39
The slope is - 0.22 and the y-intercept is 25.39. A person with 0 days spent training is expected to have a race time of 25.39 minutes and the time decreases by about - 0.22 minute per each training day.
