Slopes

The slope of any given horizontal line will always be 0. This is because if you were to write the slope of a horizontal line it would be 0/x no matter what x is, the slope will always be 0. The slope of any given vertical line is undefined. This is because the actual slope of the line would be x/0 and because you can’t divide a number by 0 in math, the slope is now undefined.

Equations

The basic equation is y = (slope) x + b. To write the equation for a vertical line you need to write x = whatever the x-intercept is (meaning the point on the x-axis goes though). For example, the equation for the vertical line previous is x = 6.

Functions and Non-Functions

The easy way to tell if any given line is a function or not is by doing the vertical line test. If the line intersects the graph more than once, then the line is not a function. This means that any given vertical line will not be a function and any horizontal line will be a function.

Domain & Range

The domain of a vertical line will always be x=__ and the range of a vertical line will be y=all real #’s. The domain will just be where the line hits the x-intercept and the range will be all real #’s because it is continuously going up and down.

Example Above. Domain: x=4 Range: All Real #’s

The domain and range of a horizontal line will be the opposite of vertical. The domain of a horizontal line will be x=all real #’s and the range will be y=__. Once again the range will be where the line hits the y-intercept and the domain will be all real #’s because it is continuously going side to side.

Example Above. Domain: x= All Real #’s Range: y=4