This blog will be discussing topics about Vertical and Horizontal Lines.

Slope

A slope is a number that determines the steepness and direction of a line in a graph.

m= Rise/Run is the formula of the slope of a line given on a graph
Rise determines the change of the vertical distance. if the rise is a positive number, the line moves up, if it is negative the line moves down
Run determines the change in the horizontal distance. The run is always positive and moves from left to right.

Vertical Line

A vertical line has an undefined slope. An undefined slope means that the y value(Run) in Slope=Rise/Run=Some Value/0
Any value for Rise will be undefined as long as the Run’s value is 0
The equation for vertical lines will always be x=some value

The graph shows a vertical line that goes through the point (1,0)
the equation for the vertical line is x=1
x=1 is an undefined slope as its y value is 0.

Horizontal Line

Horizontal Lines are lines that have zero slopes. meaning that the x value is always 0 and that the line does not move up or down. Slope= Rise/Run=0/Some value. In this case the run is 1 and the Rise is 0. 0 divided by anything equals 0, meaning that is a zero slope.

a horizontal line will always have the equation y=some value
A Horizontal line that goes through the point (0,1) has the equation y=1.

y=1 has a zero slope as its x value is 0

Domain and Range

In a graph, a point is a relation. A relation is a group of ordered pairs and is used to determine where the point is located on the graph.
The first value of a relation is called a domain(the x value) and the other is range (the y value)

Function or not a function

A function is a relation where each domain(x values) corresponds to only one element in the range. range values(y values) can repeat, but domain values cannot

A one to one function is a relation where each domain corresponds to only one element in the range without repetition in the domain and range values.

To determine if a line is a function a vertical line test can be used. A vertical line test determines if there is repetition in the domain value. if the line touches more than one point at once the line is not a function.

this graph shows that there are two points on the same domain at once meaning that the line is not a function.

To determine if a line is a one to one function, a horizontal line test is used. The horizontal line test determines if there is repetition in the range(y value) of a line.

this graph shows that the line only touches one point in the graph showing that it is a one to one function.