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:  

The horizontal line will always have zero slope.  

In the form , the  term must be zero for a horizontal line.

The forms  and  are non-linear.

A constant is a fixed number that will not change.

The equation  represents a vertical line.

The only possible answer is:  

The horizontal lines have slopes of zero.  This means that the  in the slope-intercept form  would leave only the y-intercept as the part of the equation.

The value of  is any constant.

The equations that start with  are considered vertical lines.

The correct answer is:  

The slope intercept form of an equation  refers to a linear line with a certain slope and y-intercept.

In order for the line to be horizontal, the slope  must equal to zero.

Any equation in the answer choices that has an x-variable is incorrect because this either means that the equation has a existing slope, a vertical line, or it's non-linear.

The best answer is:  

A vertical line has an undefined slope.  This also means that the x-value is fixed for every y-value of the graph.

The slope intercept form for a linear equation is .  If , the slope would indicate that the line is horizontal. 

Any answer that has a  in the equation is incorrect.

The only valid answer is:  

The horizontal line will have a slope of  in the form of .

Recall that perpendicular lines have a slope that is the negative reciprocal of the original slope.

This indicates that the vertical line will have undefined slope.   Vertical lines have a fixed x-value that will not change.  

The answer that is perpendicular to a horizontal line cannot have a y-variable in the equation.

The equation  represents a pair of intersecting lines.

The only possible answer is:  

Slope is defined as rise over run. So a slope of .7 (7/10) is the same as 7 units up and 10 units over. Compare this with the slope of 7 (7/1) which is 7 units up and only 1 unit over. The vertical distance is much greater than the horizontal and thus it is steeper.