Determining Equation of Trend Line on Scatter Plot
To determine the equation of the trend line on a scatter plot, we typically look for two points through which the line passes. Once we have those points, we can use them to calculate the slope of the line and then use one of the points to find the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
From the image, it's not possible to determine the exact coordinates of the points on the trend line with absolute precision, but we can estimate based on the grid. Let's identify two points that the trend line appears to pass through.
For example, one point on the trend line seems to be approximately at (1, 1). The other point that we can infer intersects the trend line and grid line might be at (10, 9). Let's use these two estimated points to calculate the slope (m).
The slope is calculated by taking the difference in the y-values divided by the difference in the x-values:
\( m = (y_2 - y_1) / (x_2 - x_1) \)
Using our estimated points (1, 1) and (10, 9):
\( m = (9 - 1) / (10 - 1) \)
\( m = 8 / 9 \)
Now that we know the slope, we can determine the y-intercept (b) of the trend line using the y = mx + b format and one of the points. Let's use point (1, 1):
\( y = mx + b \)
\( 1 = (8/9)(1) + b \)
\( b = 1 - 8/9 \)
\( b = 1/9 \)
So, the equation of the trend line, based on our estimations, would be approximately:
\( y = (8/9)x + 1/9 \)
Keep in mind that since the exact coordinates of the points the trend line passes through are not clearly provided, the equation obtained is based on visual estimation and might not be the precise equation used to generate the trend line in the scatter plot. However, without more accurate data, this is the best estimation we can make based on the provided image.
