Question

Draw a line of best fit for the given plot.

Guess the slope of the line

• A. $5$
• B. $\frac{1}{5}$
• C. $-5$
• D. $-\frac{1}{5}$

Answer 1

The correct option is D $-\frac{1}{5}$

A trend line is a line around which all the given points are equally scattered.

The trend line that captures the essence of the data is called the line of best fit.
$\therefore$ The line of best fit can be depicted as follows:
We can see that with increase in $x,y$ decreases.
$\therefore$ The correlation is negative.
Hence, slope of the line is negative.

$\to$ Possible options are (c) and (d).

From the figure, the line passes through $(x_1,y_1)=(1,2)$
Equation of line in point form is
$y-y_1=m(x-x_1)$

Let $m=-5$,
$\Rightarrow y-2=-5(x-1)$
Substituting $x=2$
$\Rightarrow y-2=-5(2-1)=-5\left(1\right)=-5$
$\Rightarrow y=-5+2=-3$

However, from the graph, for $x=2,y$ is positive.
$\therefore$ The assumption $m=-5$ is wrong.

Hence, option (d) is correct.