Algebra II : Vertical and Horizontal Lines

Example Questions

Example Question #1 : Vertical And Horizontal Lines

Which of the following is a horizontal line?

Explanation:

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where  is a constant. Horizontal lines have a slope of . The only equation of this form is

Example Question #1 : Vertical And Horizontal Lines

Which of the following equations represents a line that is perpendicular to ?

Explanation:

The equation  is a vertical line, so the perpendicular line must be horizontal. The only answer choice that is a horizontal line is .

Example Question #3 : Vertical And Horizontal Lines

Which of the following is a vertical line?

Explanation:

A vertical line has infinitely many values of  but only one value of . Thus, vertical lines are of the form , where  is a real number. The only equation of this form is

Example Question #1 : Vertical And Horizontal Lines

Which of the following answers describes the graph of this equation?

Not enough information

horizontal line

vertical line

vertical line

Explanation:

The graph of x=5 is a vertical line. The equation x=5 represents all points with x- value equal to 5.

Try to plot a couple of points with an x-value of 5.

A few examples are (5, 0), (5, 2), (5,5).

Draw a line connecting the points and you obtain a vertical line intercepting the x-axis at (5,0).

Example Question #5 : Vertical And Horizontal Lines

Which of the following is an equation of a vertical line?

Explanation:

Think about the meaning of a vertical line on the coordinate grid. The  value changes to any value, yet the  value always stays the same. Thus, we are talking about an equation in which the  is free, or is not effected, and the  is constant. This is an equation of the form , where  is a constant.

Example Question #6 : Vertical And Horizontal Lines

Which of the following is an equation of a horizontal line?

Explanation:

Think about what it means to be a horizontal line. The  value changes to be any real number, but the  value always remains constant. Thus, we are looking for an equation in which the  value is constant and the   value is not present. This would be any equation of the form , where  is a constant.

Example Question #7 : Vertical And Horizontal Lines

I)

II)

III)

IV)

Which of the presented equations are vertical lines?

III and IV

I and II

I

II and IV

I and III

I and III

Explanation:

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.

Example Question #1 : Vertical And Horizontal Lines

What is the equation for the horizontal line containing the point ?

Explanation:

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

Example Question #9 : Vertical And Horizontal Lines

What is the equation for the vertical line containing the point   ?

Explanation:

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,

.

Example Question #1 : Linear Functions

What is the slope of a vertical line?