A vertical line is only dependent on  and is completely independent of . Therefore, since I is , I is a vertical line. II is not a vertical line since it is only dependent upon ; it is in fact a horizontal line.

For III, if we simplify the equation

it becomes

and finally

Since III is only dependent upon , III is a vertical line.

IV is codependent upon both  and , so it is neither a vertical nor a horizontal line. Therefore, only I and III are vertical lines.

The equation for a horizontal line is 

where b is the y-coordinate of the point  on the line.

As such, the equation for the line containing the point (7, 10) is

The equation for a vertical line is  where  is the -coordinate of the point  on the line.

As such, the equation for the line containing the point  is,

.

The slope of a line is defined as the change in the y direction divided by the change in the x direction. A vertical line does not change in the y direction nor the x direction. This means that it's slope is . It is impossible to divide any number by zero, therefore the answer is undefined.

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.