Question

A scatterplot graph shows x-axis ranging from 0 to 50 and y-axis ranging from 0 to 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The x-axis is drawn in increments of 5 but labeled in increments of 10. The y-axis is drawn in increments of 1 but labeled in increments of 2. The line passes approximately through left parenthesis 0 comma 8 right parenthesis, left parenthesis 10 comma 6 right parenthesis, left parenthesis 15 comma 5 right parenthesis, left parenthesis 20 comma 4 right parenthesis, left parenthesis 25 comma three right parenthesis, and left parenthesis 40 comma 0 right parenthesis. 14 points are plotted close to or on 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 y-intercept.

We can determine the slope by using two points on the line. Let's use the points (0, 8) and (40, 0).

slope = (y2 - y1) / (x2 - x1)
= (0 - 8) / (40 - 0)
= -8 / 40
= -1/5

Now that we have the slope, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Let's use the point (0, 8):

y - 8 = -1/5(x - 0)
y - 8 = -1/5x

To put it in slope-intercept form (y = mx + b), we need to isolate y:

y = -1/5x + 8

Therefore, the equation of the trend line in slope-intercept form is y = -1/5x + 8.