Jeremy surveyed students in his class about their spending habits in the school cafeteria. He used the data to create a scatterplot.

From the graph, you can first see that there is a positive slope, and a negative y intercept. That should automatically rule out the first option.next, find the slop...

To do this take the two points that are given (2,5.5) and (5,15.25) and do rise over run. This would be (15.25-5.5)/(5-2). I just put this in a calculator and found the slope to be 3.25. You automatically know the answer because the only equation with the slope 3.25 is the third one.

MrRoyal MrRoyal · Answer 2 · 2021-11-10T10:08:46+01:00

The scatterplot shows the distribution of the students' spending habit

The equation of the trend line is: [tex]\mathbf{y = 3.25x -1}[/tex]

From the scatter plot (see attachment), we have the following points:

[tex]\mathbf{(x,y) = (2,5.5)\ (5,15.25)}[/tex]

So, the slope (m) of the trend line is:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

This gives

[tex]\mathbf{m = \frac{15.25 - 5.5}{5- 2}}[/tex]

[tex]\mathbf{m = \frac{9.75}{3}}[/tex]

[tex]\mathbf{m = 3.25}[/tex]

The equation of the trend line is then calculated as:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

This gives

[tex]\mathbf{y = 3.25(x - 2) + 5.5}[/tex]

[tex]\mathbf{y = 3.25x - 6.5 + 5.5}[/tex]

[tex]\mathbf{y = 3.25x -1}[/tex]

Hence, the equation of the trend line is: [tex]\mathbf{y = 3.25x -1}[/tex]