Question

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. 5x+10
B. 5x+11
C. 1/5x+10
D. 1/5x+11

Answer 1

To determine the equation of the line of best fit, we can use the formula for a line, y = mx + b, where m represents the slope and b represents the y-intercept.

To find the best fit line, we need to calculate the average of the x-values and the average of the y-values. Then we can use these averages to find the equation of the line.

Average of x-values = (2 + 3 + 5 + 8 + 10 + 12 + 13 + 17 + 18) / 9 = 10
Average of y-values = (9 + 12 + 11 + 13 + 12 + 11 + 14 + 12 + 15) / 9 = 12

Next, we can choose any two points from the given data points and calculate the slope. Let's choose the points (2, 9) and (18, 15) to calculate the slope.

Slope = (y2 - y1) / (x2 - x1)
= (15 - 9) / (18 - 2)
= 6 / 16
= 3/8

Now that we have the slope and the average x and y-values, we can plug them into the equation y = mx + b and solve for b.

12 = (3/8)(10) + b
12 = 30/8 + b
12 - 30/8 = b
96/8 - 30/8 = b
66/8 = b
8.25 = b

Therefore, the equation of the line of best fit that Shane drew is y = (3/8)x + 8.25.

However, none of the given answer choices match this equation.