Which of the following represents a horizontal line?

A horizontal line can be thought of as one which has the same y value for every possible value of x. In other words, it is a straight line which does not rise or fall and just remains flat at the same y-value for ever in all directions. 

Rule out any choices with a variable (x for instance), and you are left with only two options. 

Choose option:  , because regardless of the location in x, y will always be the same. 

Option:  is a vertical line, because for all values of y, x will always be the same.

A vertical line on the graph must have all the points connected such that only the y-values can change, but not the x value.  The value of  must remain constant.

If the equation starts with a  variable, and the equation is in slope intercept form, , the equation of the function would either be slanted with a positive or negative slope or horizontal, but cannot be vertical.

The equations  and  are not linear.

The only valid answer is:  

Write the slope intercept form.

For a line to be horizontal, the value of , or slope, must be zero.  The value of , or the y-intercept can be any constant number.

If the line is described by , and has no  variable,  the line will be vertical.

The only answer that will be horizontal is:  

By definition this is a vertical line and all vertical lines have a slope that is undefined.

Horizontal lines are written as the funciton y= a number.

The two lines that demonstrate this are II. and V.

By definition, a vertical line is written as x=a number.

None of these equations are written in this format so your answer is None of the above.

Step 1: We need to determine the difference between horizontal and vertical lines.

Horizontal lines have an equation, .
Vertical Lines have an equation, .

Step 2: We want the answer that is not a horizontal line. There are three equations with  and  with . The  is the odd one out.

The line that is not horizontal is 

Any equation given that has a y-variable in the equation is incorrect.  For a line to be vertical, the constant of the x-value cannot change.

This indicates that  in order to be a vertical line.

The answer is:  

Shifting a vertical line up two spaces will not change the equation.   However, shifting the vertical line four spaces to the right will change equation.

Add four to the equation.

The equation becomes:  

The answer is:  

In order for a line to be considered horizontal, there must be zero slope.

In the slope-intercept equation, , the value of  must be zero.

The answers that have an existing slope are incorrect.

The equation  is a step function, and is not a horizontal line.

The only answer that satisfies a horizontal line is:  

The answer is: