Q24. - Algebra 2

Question

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

24. $\left(\frac{1}{2},\frac{2}{3}\right),\left(\frac{5}{6},\frac{1}{4}\right)$

Step-by-Step Solution

Answer

The slope of the line is $-\frac{5}{4}$.

Step 1- Given information

A pair of points $\left(\frac{1}{2},\frac{2}{3}\right),\left(\frac{5}{6},\frac{1}{4}\right)$.

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, $(x_1,y_1)=\left(\frac{1}{2},\frac{2}{3}\right){\text{ and (x}}_2,y_2)=\left(\frac{5}{6},\frac{1}{4}\right)$

So,  $m=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}\Rightarrow m=\frac{\frac{1}{4}-\frac{2}{3}}{\frac{5}{6}-\frac{1}{2}}\\ \Rightarrow m=\frac{\frac{3-8}{12}}{\frac{5-3}{6}}\\ \Rightarrow m=\frac{\frac{-5}{12}}{\frac{2}{6}}\\ \Rightarrow m=\frac{-5\times 6}{12\times 2}\\ \Rightarrow m=-\frac{5}{4}\end{array}$

Hence, the slope of the line is $-\frac{5}{4}$.