Using this slope and the given point, we can find the equation for the line. A line passes through the points —2, 6 and 4, 5. Find the equation of a line that is perpendicular and passes through the point 4, 5. A line passes through the points, —2, —15 and 2, —3.
Find the equation of a perpendicular line that passes through the point, 6, 4. Improve this page Learn More. Skip to main content. Module 7: Linear and Absolute Value Functions. Search for:. Parallel and Perpendicular Lines Learning Outcomes Determine whether lines are parallel or perpendicular given their equations Find equations of lines that are parallel or perpendicular to a given line.
Parallel lines. Perpendicular lines. Two lines are perpendicular lines if they intersect at right angles. Example: 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. Analysis of the Solution A graph of the lines is shown below. How To: Given the equation of a linear function, write the equation of a line WHICH passes through a given point and is parallel to the given line.
Find the slope of the function. Substitute the slope and given point into point-slope or slope-intercept form. Show Solution The slope of the given line is 3. Analysis of the Solution We can confirm that the two lines are parallel by graphing them. How To: Given the equation of a linear function, write the equation of a line WHICH passes through a given point and is Perpendicular to the given line. Find the slope of the given function. Determine the negative reciprocal of the slope.
Solve for b. Write the equation of the line. Analysis of the Solution A graph of the two lines is shown below. How To: Given two points on a line and a third point, write the equation of the perpendicular line that passes through the point. Determine the slope of the line passing through the points. Once again we are going to be using material from our math past to help find the new concept.
You will need to know how to find the slope of a line given an equation and how to write the equation of a line. If you need a review on these concepts, feel free to go to Tutorial Equations of Lines. Let's see what you can do with parallel and perpendicular. Note that two lines are parallel if their slopes are equal and they have different y -intercepts. This form can be handy if you need to find the slope of a line given the equation.
Slope of the parallel line: Since parallel lines have the same slope what do you think the slope of any parallel line to this line is going to be?
Pat yourself on the back if you said Slope of the perpendicular line: Since the slopes of perpendicular lines are negative reciprocals of each other, what do you think the slope of any perpendicular line to this line is?
Slope of the parallel line: Since parallel lines have the same slope what do you think the slope of the parallel line is going to be? Slope of the perpendicular line: Since the slopes of perpendicular lines are negative reciprocals of each other, what do you think the slope of the perpendicular line is?
What is the slope of a vertical line? If you said undefined, you are right on. Slope of the parallel line: Since parallel lines have the same slope, what do you think the slope of the parallel line is going to be? Pat yourself on the back if you said undefined. Slope of the perpendicular line: Since slopes of perpendicular lines are negative reciprocals of each other, what do you think the slope of the perpendicular line is?
This one is a little trickier. Vertical lines and horizontal lines are perpendicular to each other. The slope of the perpendicular line in this case would be the slope of a horizontal line which would be 0. The slope of the parallel line is undefined and the slope of the perpendicular line is 0.
What is the slope of a horizontal line? If you said 0, you are right on. Pat yourself on the back if you said 0. The slope of the perpendicular line in this case would be the slope of a vertical line which would be undefined.
The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. A line going through the point and having slope of m would have the equation. I'm claiming that these are parallel lines. And now, I'm gonna draw some transversals here.
So first let me draw a horizontal transversal. So, just like that. And then let me do a vertical transversal. And I'm assuming that the green one is horizontal and the blue one is vertical. So we assume that they are perpendicular to each other, that these intersect at right angles. And from this, I'm gonna figure out, I'm gonna use some parallel line angle properties to establish that this triangle and this triangle are similar and then use that to establish that both of these lines, both of these yellow lines have the same slope.
So actually let me label some points here. So, let's see. So that's a right angle and then that is a right angle right over there. We also know some things about corresponding angles for where our transversal intersects parallel lines.
This angle corresponds to this angle if we look at the blue transversal as it intersects those two lines. And so they're going to be, they're going to have the same measure, they're going to be congruent. Now this angle on one side of this point B is going to also be congruent to that, because they are vertical angles. We've seen that multiple times before. Sometimes this is called alternate interior angles of a transversal and parallel lines.
Well, if you look at triangle CED and triangle ABE, we see they already have two angles in common, so if they have two angles in common, well, then their third angle has to be in common.
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