Q21. - Algebra 1

Question

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

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

Step-by-Step Solution

Answer

The number 6 represents the required slope.

Step 1. Determine the formula that can be used.

The slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ can be used to calculate the required slope.

Step 2. Take the help of the obtained method.

Take the help of formula for slope of a line represented by $m=\frac{y_2-y_1}{x_2-x_1}$ in which the required values can be filled by using the provided points as they are in the form of $\left(x_1,y_1\right) \left(x_2,y_2\right)$.

 $\begin{array}{c}m=\frac{\frac{1}{4}-\frac{3}{4}}{\frac{2}{3}-\frac{3}{4}}\\ =\frac{\frac{1-3}{4}}{\frac{8-9}{12}}\\ =\frac{\frac{-2}{4}}{\frac{-1}{12}}\\ =\frac{-2}{4}\times \frac{-12}{1}\\ =\frac{24}{4}\\ =6\end{array}$

Step 3. Write the conclusion.

The obtained slope is 6. So, it is the required slope.