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.

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semsee45 semsee45 · Answer 1 · 2022-11-11T13:11:12+01:00

Answer:

[tex]\hat{y}=-0.29x+5.67[/tex]

Step-by-step 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:

[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]