Question

A scatter plot along with the line of best fit of $x$ and $y$ is shown below.
Determine the equation and slope of the line of best fit.

• A. $12y=5x-26$
• B. $12y=5x-56$
• C. Slope $=\frac{25}{12}$
• D. Slope $=\frac{5}{12}$

Answer 1

Answer: (A), (D)

Slope $=\frac{5}{12}$

It is given that the blue line is line of best fit and we need to find it's equation.
From the figure, the line passes through the points $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(8,5.5)$

Slope of the line, $m$
$=\frac{y_2-y_1}{x_2-x_1}$
$=\frac{5.5-3}{8-2}$
$=\frac{2.5}{6}$
$=\frac{25}{6\times 2\times 5}$
$=\frac{5}{12}$

Equation of line in point form is
$y-y_1=m(x-x_1)$
Substituting point $(2,3)$ in the equation
$\Rightarrow y-3=\frac{5}{12}(x-2)$
$\Rightarrow 12(y-3)=5(x-2)$
$\Rightarrow 12y-36=5x-10$
$\Rightarrow 12y=5x-10+36$
$\Rightarrow 12y=5x+26$

Hence, the equation of the line is $12y=5x+26$ with slope $=\frac{5}{12}.$