Question

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 10 in increments of 1. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 8 comma 7 right parenthesis, and left parenthesis 10 comma 6.5 right parenthesis. 12 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

Answer 1

To find the equation of the trend line, we need to determine the slope and the y-intercept.

To calculate the slope, we can use any two points on the line, such as (0,9) and (8,7).

Slope (m) = (y2 - y1) / (x2 - x1)
= (7 - 9) / (8 - 0)
= -2 / 8
= -1/4

The slope of the trend line is -1/4.

Next, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

Using the point (0,9) on the line:

y = mx + b
9 = (-1/4)(0) + b
9 = 0 + b
b = 9

The y-intercept (b) is 9.

Therefore, the equation of the trend line in slope-intercept form is:

y = -1/4x + 9