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Chapter 2: Q24. (page 72)

Find the slope of the line that passes through each pair of points.
24. $(\frac{1}{2}, \frac{2}{3}), (\frac{5}{6}, \frac{1}{4})$

Short Answer

Expert verified

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

Step by step solution

01

Step 1- Given information

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

02

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 $(x_{1}, y_{1}), (x_{2}, y_{2}) and x_{1} 鈮� x_{2} .$

03

Step 3- To find the slope

Here, $(x_{1}, y_{1}) = (\frac{1}{2}, \frac{2}{3}) {and (x}_{2}, y_{2}) = (\frac{5}{6}, \frac{1}{4})$

So, $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$\begin{array}{l} 鈬� m = \frac{\frac{1}{4} - \frac{2}{3}}{\frac{5}{6} - \frac{1}{2}} \\ 鈬� m = \frac{\frac{3 鈭� 8}{12}}{\frac{5 鈭� 3}{6}} \\ 鈬� m = \frac{\frac{鈭� 5}{12}}{\frac{2}{6}} \\ 鈬� m = \frac{鈭� 5 脳 6}{12 脳 2} \\ 鈬� m = - \frac{5}{4} \end{array}$

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

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