Question

Find the slope of the line that passes through each pair of points.

$\left(\frac{1}{2},-\frac{1}{3}\right),\left(\frac{1}{4},\frac{2}{3}\right)$

Short answer

The slope of the line is $-4$.

Step-by-step solution

Step 1- Given information

A pair of points $\left(\frac{1}{2},-\frac{1}{3}\right),\left(\frac{1}{4},\frac{2}{3}\right)$.

Step 2- Formula used

The slope formula of a line is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where, m is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{and}{x}_1\ne x_2.$

Step 3- To find the slope 

Here, $(x_1,y_1)=\left(\frac{1}{2},-\frac{1}{3}\right){\text{and (x}}_2,y_2)=\left(\frac{1}{4},\frac{2}{3}\right)$

So, $m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}\Rightarrow m=\frac{\frac{2}{3}-(-\frac{1}{3})}{\frac{1}{4}-\frac{1}{2}}\\ \Rightarrow m=\frac{\frac{2}{3}+\frac{1}{3}}{\frac{1}{4}-\frac{1}{2}}\\ \Rightarrow m=\frac{1}{\frac{1-2}{4}}\\ \Rightarrow m=-4\end{array}$

Hence, the slope of the line is $-4$.