Question

The scatter plot shows the winning times, in seconds, in a 50-meter race over eight consecutive years.

Scatter plot with x axis labeled Time in Years and y axis labeled Winning Time with points at 1 comma 5 and 4 tenths, 2 comma 5, 3 comma 4 and 6 tenths, 4 comma 4 and 9 tenths, 5 comma 4 and 1 tenth, 6 comma 3 and 9 tenths, 7 comma 3 and 6 tenths, and 8 comma 3 and 3 tenths.

Which of the following is an appropriate line of best fit?

y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
y hat equals 29 hundredths times x plus 5 and 67 hundredths.
y hat equals negative 45 hundredths times x plus 7 and 69 hundredths.
y hat equals 45 hundredths times x plus 7 and 69 hundredths.

Answer 1

`\hat{y}=-0.29x+5.67`

Explanation:

Given points on the scatter plot:

• (1, 5.4)
• (2, 5)
• (3, 4.6)
• (4, 4.9)
• (5, 4.1)
• (6, 3.9)
• (7, 3.6)
• (8, 3.3)

Plot the given points and draw a line of best fit (see attachment).

As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.

From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.

Therefore, the equation that is appropriate for the line of best fit is:

`\boxed{\hat{y}=-0.29x+5.67}`