Lesson 2: Linear Functions

Property

The slope-intercept form for a linear equation is $y = mx + b$, where $m$ is the slope of the line and the point $(0, b)$ is the y-intercept.

The slope formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$.

This formula calculates the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run).

Property

The slope of a line is constant: no matter which two points you pick to compute the slope, you will always get the same value.

Because $m$ is constant for a given line, we can use the formula $m = \frac{\Delta y}{\Delta x}$ to find $\Delta y$ when we know $\Delta x$, or to find $\Delta x$ when we know $\Delta y$.

We can also tell whether a collection of data points lies on a straight line by computing slopes between them.