Algebra II : Vertical and Horizontal Lines

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #831 : Algebra Ii

Which of the following graphs exhibit a horizontal line?

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #22 : Linear Functions

Which of the following is a horizontal line?

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #23 : Linear Functions

Which of the following equations will represent a horizontal line?

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #24 : Linear Functions

Which of the following answers is considered a vertical line?

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #25 : Linear Functions

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

Possible Answers:

Correct answer:

Explanation:

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:  

Example Question #832 : Algebra Ii

Which of these lines is the steepest or would be most difficult to walk up if the line represented a ramp?

Possible Answers:

Correct answer:

Explanation:

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. 

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