Question

a scatter plot was made to show the record for the 100 - meter dash over several years at meander high school. the equation of the scatter plots trend line is ( y = - 0.14x + 12.5 ) where ( y ) is the record in seconds, and ( x ) is the number of years since the year 2000. use the trend line equation to predict the year that the record for the 100 - meter dash was 11.8 seconds. a. 2005 b. 2010 c. 2011 d. 1995

Explanation:

Step1: Substitute \( y = 11.8 \) into the equation

Given \( y=-0.14x + 12.5 \), substitute \( y = 11.8 \):
\( 11.8=-0.14x + 12.5 \)

Step2: Solve for \( x \)

Subtract \( 12.5 \) from both sides:
\( 11.8-12.5=-0.14x \)
\( - 0.7=-0.14x \)
Divide both sides by \( - 0.14 \):
\( x=\frac{-0.7}{-0.14}=5 \)

Step3: Find the year

Since \( x \) is the number of years since 2000, the year is \( 2000 + x \). Substitute \( x = 5 \):
\( 2000+5=2005 \)

Answer:

A. 2005