Vertical and Horizontal Lines - Algebra II
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Which of the following is a vertical line?
Which of the following is a vertical line?
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 
.
A vertical line has infinitely many values of
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Which of the following is a horizontal line?
Which of the following is a horizontal line?
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 
.
A horizontal line has infinitely many values for
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Which of the following equations represents a line that is perpendicular to 
?
Which of the following equations represents a line that is perpendicular to
The equation 
is a vertical line, so the perpendicular line must be horizontal. The only answer choice that is a horizontal line is 
.
The equation
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I) 
II) 
III) 
IV) 
Which of the presented equations are vertical lines?
I)
II)
III)
IV)
Which of the presented equations are vertical lines?
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.
A vertical line is only dependent on
For III, if we simplify the equation
it becomes
and finally
Since III is only dependent upon
IV is codependent upon both
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Which of the following answers describes the graph of this equation?
(Select all answers that apply)
Which of the following answers describes the graph of this equation?
(Select all answers that apply)
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).
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).
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Which of the following is an equation of a vertical line?
Which of the following is an equation of a vertical line?
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.
Think about the meaning of a vertical line on the coordinate grid. The
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Which of the following is an equation of a horizontal line?
Which of the following is an equation of a horizontal line?
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.
Think about what it means to be a horizontal line. The
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What is the equation for the vertical line containing the point 
?
What is the equation for the vertical line containing the point
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 equation for a vertical line is
As such, the equation for the line containing the point
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What is the equation for the horizontal line containing the point 
?
What is the equation for the horizontal line containing the point
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 horizontal line is
where b is the y-coordinate of the point
As such, the equation for the line containing the point (7, 10) is
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What is the slope of a vertical line?
What is the slope of a vertical line?
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.
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
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Which of the following represents a horizontal line?
Which of the following represents a horizontal line?
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.
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:
Option:
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Which of the following equations will exhibit a vertical line when graphed?
Which of the following equations will exhibit a vertical line when graphed?
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: 
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
If the equation starts with a
The equations
The only valid answer is:
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What is the slope of the line 
?
What is the slope of the line
By definition this is a vertical line and all vertical lines have a slope that is undefined.
By definition this is a vertical line and all vertical lines have a slope that is undefined.
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Which of the following equation exhibits a horizontal line?
Which of the following equation exhibits a horizontal line?
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: 
Write the slope intercept form.
For a line to be horizontal, the value of
If the line is described by
The only answer that will be horizontal is:
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Which of the following are horizontal lines?
I. 
II. 
III. 
IV. 
V. 
Which of the following are horizontal lines?
I.
II.
III.
IV.
V.
Horizontal lines are written as the funciton y= a number.
The two lines that demonstrate this are II. and V.
Horizontal lines are written as the funciton y= a number.
The two lines that demonstrate this are II. and V.
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Which of the following is a vertical line?
I. 
II. 
III. 
Which of the following is a vertical line?
I.
II.
III.
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.
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.
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Which one of the following equations is NOT a horizontal line?
Which one of the following equations is NOT a horizontal line?
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 
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
The line that is not horizontal is
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Which of the following equations represent a vertical line?
Which of the following equations represent a vertical line?
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: 
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
The answer is:
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Shift the line 
up two spaces and right four spaces. What is the new equation?
Shift the line
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: 
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:
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Which of the following equations represent a horizontal line?
Which of the following equations represent a horizontal line?
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: 
In order for a line to be considered horizontal, there must be zero slope.
In the slope-intercept equation,
The answers that have an existing slope are incorrect.
The equation
The only answer that satisfies a horizontal line is:
The answer is:
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