Question

What is the slope of the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$?

• A. $\frac{y_1}{x_2-x_1}$
• B. $\frac{y_2-y_1}{x_2-x_1}$
• C. $\frac{y_2}{x_1-x_2}$
• D. $\frac{y_2}{x_2}$

Answer 1

The correct option is B $\frac{y_2-y_1}{x_2-x_1}$

Slope of a line is defined as the ratio of the rise to the run.

In the figure given, the two points are $(x_1,y_1)$ and $(x_2,y_2)$.

As we can see, the rise, which is the change in the y coordinate is $y_2-y_1$

and, the run, which is the change in the x coordinate is $x_2-x_1$

Thus,
$\text{slope}=\frac{\text{rise}}{\text{run}}$
$=\frac{y_2-y_1}{x_2-x_1}$