Question

Find if possible, the slope of the line through the points $(1/2,3/4)$ and $(-1/3,5/4)$

Answer 1

Since slope of line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

We now find the slope of the line passing through the points $(\frac{1}{2},\frac{3}{4})$ and $(-\frac{1}{3},\frac{5}{4})$ as shown below:

$m=\frac{\frac{5}{4}-\frac{3}{4}}{-\frac{1}{3}-\frac{1}{2}}=\frac{\frac{2}{4}}{-\frac{5}{6}}=\frac{\frac{1}{2}}{-\frac{5}{6}}=\frac{1}{2}\times -\frac{6}{5}=-\frac{6}{10}=-\frac{3}{5}$

Therefore, the slope of the line is $-\frac{3}{5}$.