Perpendicular lines cross each other at a degree angle. Both sets of lines are important for many geometric proofs, so it is important to recognize them graphically and algebraically.
Slopes of parallel and perpendicular lines Video transcript We're asked what is the equation of line B? And they tell us that line A has an equation y is equal to 2x plus And they say that the line B contains the point 6, negative 7.
And they tell us lines A and B are perpendicular, so that means that slope of B must be negative inverse of slope of A. So what we'll do is figure out the slope of A, then take the negative inverse of it.
Then we'll know the slope of B, then we can use this point right here to fill in the gaps and figure out B's y-intercept. So what's the slope of A? This is already in slope-intercept form.
The slope of A is right there, it's the 2, mx plus b. So the slope here is equal to 2. So the slope of A is 2. What is the slope of B? So what is B's slope going to have to be? Well, it's perpendicular to A, so it's going to be the negative inverse of this.
So we know that B's equation has to be y is equal to its slope, m times x plus some y-intercept. We still don't know what the y-intercept of B is, but we can use this information to figure it out. We know that y is equal to negative 7 when x is equal to 6.
I just know that this is on the point, so this point must satisfy the equation of line B. So let's work out what b must be-- or what b, the y-intercept, this is a lowercase b, not the line B.
That's not a b there, that's a 6.
It's negative 3, is equal to negative 3 plus our y-intercept. Let's add 3 to both sides of this equation, so if we add 3 to both sides-- I just want to get rid of this 3 right here-- what do we get?
The left-hand side, negative 7 plus 3 is negative 4, and that's going to be equal to-- these guys cancel out-- that's equal to b, our y-intercept. So this right here is a negative 4. And its y-intercept we just figured out is negative 4. And we are done.Find an equation of the line through the points (-3, 5) and (9, 10) and write it in the standard form Ax + By = C, with A > 0.
Questions Find an equation of the line parallel to the line 3x + 6y = 5 and passing through the point (1, 3). 2x+y-5=0;(0,4)write the standard form of the equation of the line that is parallel to the graph of the given equation and that passes through the point with the given coordinate.
Writing Slope-Intercept Form Given the Perpendicular Line and a Point Writing Standard Form Given Parts Writing Standard Form Given the Graph of the Line Solving Word Problems Involving Writing Equations Overview Writing Equations to Model Real-World Situations Writing Standard Form Given Parts — Writing Standard Form Given the Graph of.
Problem: Write an equation of the line that passes through (0, 2) and is parallel to the line which passes through (7, 12) and (3, - 1). y = x + 2 Problem: Write an equation of the line that passes through the origin and is perpendicular to the line 3 y + 4 x = 0.
Write the equation of the given line in slope-intercept form to determine its slope, then use the opposite reciprocal of that slope and your point in the point-slope formula Let's look at some examples.
Overview of different forms of a line's equation. There are many different ways that you can express the equation of a leslutinsduphoenix.com is the slope intercept form, point slope form and also this page's topic.
Each one expresses the equation of a line, and each one has its own pros and cons.