We are given a table that shows the numbers of students at a middle school over a ten-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. We can use the points (1,492) and (6,562).
The slope of the line is 14. With this information, we can write its partial equation in slope-intercept form.
y= 14x+b
To find the y-intercept b, we will use the fact that the line passes through the point (1,492). We will substitute 1 for x and 492 for y, then solve for b.
The y-intercept of the line is 478. We have all the information we need to write the equation of the line!
y=14x+ 478
Let's consider the equation we obtained in Part B. Recall that in our case, x represents the year and y represents the number of students at a middle school.
y= 14x+ 478
We can interpret each part of this equation in the given context.
A slope of 14 means that the number of students increases by about 14 people per year.
A y-intercept of 478 means that in a year before the ten-year period there were 478 students in a middle school.
We want to predict the number of students in a middle school in year 11. To do this, we will substitute 11 for x into the equation of the line of fit. Then, we will find the value of y.
