Example Question - scatter plot analysis
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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.
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.
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