Perpendicular lines have negative reciprocal slopes. Figure Skip to main content. Graphs of Linear Functions. Search for:. Given the equations of two lines, determine whether their graphs are parallel or perpendicular The two lines in Figure 18 are parallel lines : they will never intersect. Parallel lines. Perpendicular lines. Example 8: Identifying Parallel and Perpendicular Lines Given the functions below, identify the functions whose graphs are a pair of parallel lines and a pair of perpendicular lines.
Solutions Parallel lines have the same slope. Analysis of the Solution A graph of the lines is shown in Figure Licenses and Attributions. The slope of one line is the negative reciprocal of the slope of the other line. The product of a number and its reciprocal is 1. To find the reciprocal of a number, divide 1 by the number. To find the negative reciprocal, first find the reciprocal and then change the sign.
As with parallel lines, we can determine whether two lines are perpendicular by comparing their slopes. The slope of each line below is the negative reciprocal of the other so the lines are perpendicular.
Two lines are parallel lines if they do not intersect. The slopes of the lines are the same. Coincident lines are the same line. Given the functions below, identify the functions whose graphs are a pair of parallel lines and a pair of perpendicular lines. Parallel lines have the same slope. Perpendicular lines have negative reciprocal slopes. If we know the equation of a line, we can use what we know about slope to write the equation of a line that is either parallel or perpendicular to the given line.
We know that the slope of the line is 3. We also know that the y- intercept is 0, 1. Any other line with a slope of 3 will be parallel to f x. The lines formed by all of the following functions will be parallel to f x. Suppose then we want to write the equation of a line that is parallel to f and passes through the point 1, 7. We already know that the slope is 3. We just need to determine which value for b will give the correct line.
We can begin by using point-slope form of an equation for a line. We can then rewrite it in slope-intercept form. The slope of the given line is 3. We can confirm that the two lines are parallel by graphing them. The figure below shows that the two lines will never intersect. We can use a very similar process to write the equation of a line perpendicular to a given line.
Instead of using the same slope, however, we use the negative reciprocal of the given slope. Suppose we are given the following function:. Email address: Your name:. Possible Answers:. Correct answer:. Report an Error. Explanation : When two lines are parallel, they have the same slope. Explanation : Parallel lines have identical slopes. Which equation described a line parallel to the line that connects points —8,9 and 3,—4? Explanation : In order for two lines to be parellel, their slopes have to be the same.
Which of the following are NOT parallel to each other? Explanation : Four of the answers are not in slope-intercept form. For the lines to be parallel, all must share the same slopes. To identify the slopes, this is the term of: The only equation that does not have a slope of is. Explanation : If two lines are parallel, then they have the same slope. Line A is: Rewrite this in slope-intercept form where is the slope: The slope of line A is. Find the slope of a line parallel to the line with the equation:.
Explanation : Lines can be written in the slope-intercept format: In this format, equals the line's slope and represents where the line intercepts the y-axis. In the given equation: And it has a slope of: Parallel lines share the same slope. Copyright Notice. View Algebra Tutors. William M. Certified Tutor. Luther College, Bachelor in Arts, Mathematics. Natkai Certified Tutor. Radford University, Bachelor of Science, Psychology.
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