1.10: Lines

In Calculus I, you study something called a derivative.

In simple terms, the derivative is the slope of particular type of line.

Let's talk about slopes.

The slope of a line that runs through two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $$m=\text{slope}={\displaystyle \frac{\text{rise}}{\text{run}}}={\displaystyle \frac{y_2-y_1}{x_2-x_1}}$$

The slope of a line that runs through two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $$m=\text{slope}={\displaystyle \frac{\text{rise}}{\text{run}}}={\displaystyle \frac{y_2-y_1}{x_2-x_1}}$$

There are four possible slopes, depending on the rise:

Point-Slope Form of a Line

To define a line, you only need one point and a slope.

Vertical and Horizontal Lines