Given the data set (5, 9), (13, 12), (23, 16), which of the following equations best represents a line of best fit?
y = three fourths x − 7
y = four fifths x + 7 ***
y = three over two x + 7
y = two thirds x − 7
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It's see
To determine which equation best represents a line of best fit for the given data set, we can use the method of calculating the slope and y-intercept.
The equation for a line is in the form y = mx + b, where m represents the slope and b represents the y-intercept.
To calculate the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given data points:
First data point: (5, 9)
Second data point: (13, 12)
m = (12 - 9) / (13 - 5)
m = 3 / 8
m = 0.375
The slope of the line is approximately 0.375.
Now, let's calculate the y-intercept (b) using one of the data points and the slope:
Using the first data point (5, 9):
y = mx + b
9 = (0.375)(5) + b
9 = 1.875 + b
b = 9 - 1.875
b = 7.125
The y-intercept (b) is approximately 7.125.
Therefore, the equation that represents the line of best fit is y = (0.375)x + 7.125.
Looking at the given options, the equation that matches the line of best fit for the data set is y = four fifths x + 7.