Answer: To draw a trend line that models the given data set, we first need to plot the points on a graph. We can use a scale of 1 unit on the x-axis and 5 units on the y-axis to plot the points as follows:
(1, 27.5) ●
(4, 35) ●
(7, 42.5) ●
(10, 50) ●
(13, 57.5) ●
We can see that the points roughly form a straight line. To find the equation of the trend line, we can use linear regression, which involves finding the line that best fits the data.
Using a calculator or software, we can find that the equation of the trend line is:
y = 3.5x + 24
This means that for every increase of 1 unit in x, y increases by 3.5 units. The y-intercept of the trend line is 24, which represents the value of y when x = 0.
We can plot the trend line on the same graph as follows:
|
60 |-●-
| |
55 |-●-----
| |
50 |-●-------
| |
45 |-●--------
| |
40 |-●----------
| |
35 |-●------------
| |
30 |-●--------------
| |
25 |-●-----------------
| |
--------------------
1 4 7 10 13
The dots represent the original data points, and the line represents the trend line.
Explanation: