Determining Equation of Trend Line in Scatter Plot with Two Points
To determine the equation of the trend line in a scatter plot, you usually need two points on the line to find the slope and then use one of these points to solve for the y-intercept.
From the image provided, we can identify two points on the trend line. Let's select two points that clearly lie on the line and are easy to read:
Point 1 (on the left end of the line): It looks like it crosses the y-axis at y = 1. This would make the point (0,1).
Point 2 (somewhere on the line where it crosses a grid intersection): It's hard to tell exactly from this image, but let's assume it's (5,5).
Next, we calculate the slope (m) using the formula:
\( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \)
Plugging in the point values:
\( m = \frac{(5 - 1)}{(5 - 0)} \)
\( m = \frac{4}{5} = 0.8 \)
With the slope of 0.8 and knowing the line crosses the y-axis at (0,1), we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Thus, the equation of the trend line is:
y = 0.8x + 1
Please note that the accuracy of this equation depends on how precisely we can read the points from the image. For a more accurate equation, a clear reading of exact points on the line or the actual data used to generate the scatter plot would be necessary.
