We are given a table that shows the numbers of people who attended a festival over an eight-year period. 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.
However, in this case, it seems that none of these points lie on the line. Therefore, we will choose two points on the line that do not belong to the given data set.
We can use the points (1,200) and (2.5,600).
The slope of the line is 266.6. With this information, we can write its partial equation in slope-intercept form.
y= 266.6x+b
To find the y-intercept b, we will use the fact that the line passes through the point (1,200). We will substitute 1 for x and 200 for y, then solve for b.
The y-intercept of the line is - 66.6. We have all the information we need to write the equation of the line!
y=266.6x+( - 66.6)
⇕
y=266.6x-66.6
Let's consider the equation we obtained in Part B. Recall that in our case, x represents the year of the festival and y represents the attendance.
y= 266.6x - 66.6
We can interpret each part of this equation in the given context.
A slope of 266.6 means that the attendance increases by about 266.6 people per year.
A y-intercept of - 66.6 does not make sense in this context — we cannot have a negative number of people in attendance. There need to be attendees for the festival to happen, so x cannot be 0.
