Answer
The slope of the line passing through the points $\left( -3,\frac{1}{4} \right)$ and $\left( 6,\frac{1}{4} \right)$ is 0 and this line is horizontal.
Work Step by Step
The slope of the line passing through two points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is provided by the formula $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$.
Now, calculate the slope of the line passing through the points $\left( -3,\frac{1}{4} \right)$ and $\left( 6,\frac{1}{4} \right)$ as shown below:
$\begin{align}
& m=\frac{\frac{1}{4}-\frac{1}{4}}{6+3} \\
& =\frac{0}{9} \\
& =0
\end{align}$
Therefore, the slope of this line is 0.
Since the slope of the line is 0, thus the line is horizontal; that is, it is parallel to the $x$ axis.
Hence, the slope of the line passing through the points $\left( -3,\frac{1}{4} \right)$ and $\left( 6,\frac{1}{4} \right)$ is 0 and this line is horizontal.
