Shane created a scatter plot and drew a line of best fit, as shown.
A scatter plot has data points (2, 9), (3, 12), (5, 11), (8, 13), (10, 12), (12, 11), (13, 14), (17, 12), and (18, 15). A diagonal fits two points. The maximum ranges of points lie above and below the curve.
What is the equation of the line of best fit that Shane drew?
A. y=5x+10
B. y=5x+11
C. y=1/5x+10
D. y=1/5x+11
To determine the equation of the line of best fit, we need to find the slope and y-intercept of the line. We can do this by using any two points from the scatter plot.
Let's use the points (2, 9) and (18, 15):
Slope = (change in y) / (change in x)
= (15 - 9) / (18 - 2)
= 6 / 16
= 3/8
Now that we have the slope, we can use the point-slope form of a straight line to find the equation:
y - y1 = m(x - x1)
Using the point (2, 9), we have:
y - 9 = (3/8)(x - 2)
Multiplying through by 8 to eliminate the fraction:
8y - 72 = 3x - 6
Simplifying:
8y = 3x + 66
y = 3/8x + 33/4
Comparing this to the answer choices, the correct equation is:
D. y=1/5x+11