Question

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Speeds versus times taken by a car to travel a certain distance are tabulated below.
Speed (mph) Time (minutes)

$30$	$120$
$40$	$95$
$50$	$85$
$60$	$60$

Choose the correct option for the line of best fit.

• A. $y+2x=120$
• B. $y-60=2(x-60)$
• C. $y+2x=180$
• D. $y-60=2(x+60)$

Answer 1

The correct option is C $y+2x=180$

Let's graph the given data set in a scatter plot with speed (independent variable) on the horizontal axis and time taken by the car to travel a certain distance (dependent variable) on the vertical axis.

Let's draw a suitable trend line that passes through two points such that it accurately captures the trend of the data set, and also equally distribute the remaining data points around the trend line.


In the above scatter plot, the cyan line is the line of best fit, which passes through the points $(x_1,y_1)=(60,60)$ and $(x_2,y_2)=(30,120)$.

$\underset{–}{\text{Note:}}$ Logically, we can conclude that if speed of the car will increase, the time taken by the car to travel a certain distance will decrease. Hence, the line of best fit also accurately signifies the trend of the given data set.

The slope of the line of best fit is
$m=\frac{y_2-y_1}{x_2-x_1}$
$\Rightarrow m=\frac{120-60}{30-60}=\frac{60}{-30}=-2$

$\underset{–}{\text{Note:}}$ The negative slope of the line of best fit signifies that speed of the car and the time taken by the car to travel a certain distance are negatively correlated.

Hence, the equation of the line of best fit is

$y-y_1=m(x-x_1)$

$\Rightarrow y-60=-2(x-60)$

$\Rightarrow y-60=-2x+120$

$\Rightarrow y-60+60=-2x+120+60$

$\Rightarrow y=-2x+180$

$\Rightarrow y+2x=-2x+180+2x$

$\Rightarrow y+2x=180$

$\therefore$ Option (c.) is the correct one.