Which equation BEST represents the line of best for the scatterplot?
y = -100x + 50
y = 100x + 24
y = 2/3x + 100
y = -3/2x + 100
y = 100/3x + 100
There is no scatterplot provided, so it is impossible to determine the equation that represents the line of best fit.
To determine which equation represents the line of best fit for the scatterplot, we need to analyze the slope and y-intercept values.
The equation y = mx + b represents a line, where m represents the slope and b represents the y-intercept.
Looking at the given options:
1. y = -100x + 50:
Slope = -100
Y-intercept = 50
2. y = 100x + 24:
Slope = 100
Y-intercept = 24
3. y = 2/3x + 100:
Slope = 2/3
Y-intercept = 100
4. y = -3/2x + 100:
Slope = -3/2
Y-intercept = 100
5. y = 100/3x + 100:
Slope = 100/3
Y-intercept = 100
The line of best fit should have a slope and y-intercept that approximate the trend shown by the scatterplot. It is difficult to determine the exact equation without visualizing the scatterplot. However, by evaluating the slope and y-intercept values, the equation that may best represent the line of best fit is:
y = 2/3x + 100.
To determine which equation represents the line of best fit for a scatterplot, we need to analyze the pattern of the plotted points.
One way to find the line of best fit is by visually inspecting the scatterplot and identifying the line that seems to pass closest to most of the points. However, this method can be subjective and prone to errors.
A more objective and accurate method is to use the method of least squares to find the equation of the line that minimizes the sum of the squared vertical distances between the points and the line.
To calculate the line of best fit using the method of least squares, follow these steps:
1. Calculate the means (average) of the x-coordinates and y-coordinates of the points.
2. Calculate the differences between each x-coordinate and the mean of x (x - x̄).
3. Calculate the differences between each y-coordinate and the mean of y (y - ȳ).
4. Multiply each pair of differences obtained in steps 2 and 3.
5. Calculate the squared differences obtained in step 4.
6. Sum the squared differences from step 5.
7. Calculate the product of the differences in x-coordinates obtained in step 2.
8. Calculate the sum of the squared differences from step 7.
9. Calculate the slope (b) of the line of best fit using the formula:
b = sum of the products of differences / sum of the squared differences from step 7.
10. Calculate the y-intercept (a) of the line using the formula:
a = ȳ - b * x̄.
11. Write the equation of the line using the slope (b) and y-intercept (a) obtained in steps 9 and 10.
Now, let's analyze the given equations:
y = -100x + 50
y = 100x + 24
y = 2/3x + 100
y = -3/2x + 100
y = 100/3x + 100
To determine which equation represents the line of best fit, we need to compare the slopes and y-intercepts of each equation with the values obtained by the method of least squares.
Without analyzing the actual scatterplot or the data points, we cannot definitively determine which equation is the best fit. The line of best fit can only be accurately determined by applying the method of least squares to the actual data.