To find the equation of the line of best fit, we can use the method of least squares. This involves finding the line that minimizes the sum of squared differences between the actual y-values and the predicted y-values.
First, we need to find the slope of the line. We can use the formula for slope: m = (y2 - y1) / (x2 - x1)
Using the points (-3, –40) and (7, 137), we can calculate the slope:
m = (137 - (-40)) / (7 - (-3))
m = 177 / 10
m = 17.7
Now that we have the slope, we can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
Using the point (1, 12), we can substitute the values of x and y into the equation to find the y-intercept:
12 = 17.7(1) + b
12 = 17.7 + b
b = 12 - 17.7
b = -5.7
So the equation of the line of best fit is y = 17.7x - 5.7.
None of the given answer choices match this equation.
Find the equation of the line of best fit for the points (−3, – 40), (1, 12), (5, 72), and (7, 137).
a. y = 3x + 17
b. y = 17x + 3
c. y = 3x + 1
d. y = x + 3
1 answer