How to write an equation in standard form given two points and slope

Slope-intercept form linear equations Standard form linear equations Point-slope form linear equations Video transcript A line passes through the points negative 3, 6 and 6, 0.

How to write an equation in standard form given two points and slope

Standard form linear equations Video transcript - [Voiceover] We've already looked at several ways of writing linear equations. You could write it in slope-intercept form, where it would be of the form of Y is equal to MX plus B, where M and B are constants.

M is the coefficient on this MX term right over here and M would represent the slope. And then from B you're able to figure out the y-intercept.

how to write an equation in standard form given two points and slope

The Y, you're able to figure out the y-intercept from this. Literally the graph that represents the XY pairs that satisfy this equation, it would intersect the y-axis at the point X equals zero, Y is equal to B. And it's slope would be M.

We've already seen that multiple times. We've also seen that you can also express things in point-slope form. So let me make it clear. And these are just different ways of writing the same equations.

You can algebraically manipulate from one to the other.

Explore the Common Core

Another way is point-slope. And in point-slope form, if you know that some, if you know that there's an equation where the line that represents the solutions of that equation has a slope M. Slope is equal to M. This is point-slope form and we do videos on that. But what I really want to get into in this video is another form.

And it's a form that you might have already seen. And that is standard form. And what I want to do in this video, like we've done in the ones on point-slope and slope-intercept is get an appreciation for what is standard form good at and what is standard form less good at?

So let's give a tangible example here. So let's say I have the linear equation, it's in standard form, 9X plus 16Y is equal to And we wanted to graph this.

So the thing that standard form is really good for is figuring out, not just the y-intercept, y-intercept is pretty good if you're using slope-intercept form, but we can find out the y-intercept pretty clearly from standard form and the x-intercept.

The x-intercept isn't so easy to figure out from these other forms right over here. So how do we do that? Well to figure out the x and y-intercepts, let's just set up a little table here, X comma Y, and so the x-intercept is going to happen when Y is equal to zero.

And the y-intercept is going to happen when X is equal to zero.

Writing Algebra Equations Given Two Points

So when Y is zero, what is X?The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and are an idealization of such objects.

Until the 17th century, lines were defined in this manner: "The [straight or curved] line is the first species of quantity, which has only one dimension, namely length, without any width.

Now I have the slope and two points. I know I can find the equation (by solving first for " b ") if I have a point and the slope; that's what I did in the previous example. Here, I have two points, which I used to find the slope.

A line passes through the points negative 3, 6 and 6, 0. Find the equation of this line in point slope form, slope intercept form, standard form.

And the way to think about these, these are just three different ways of writing the same equation.

Perpendicular Lines

So if you give me one of them, we can manipulate it to. Learn why the Common Core is important for your child. What parents should know; Myths vs. facts. After understanding the exponential function, our next target is the natural logarithm.

Given how the natural log is described in math books, there’s little “natural” about it: it’s defined as the inverse of e^x, a strange enough exponent already.

But there’s a fresh, intuitive explanation. @Aditya: Thanks! Yes, it took me a while to really see the equation, there may be a nicer way to go back and streamline how it was presented — I’d like to avoid the need for people to have multiple readings:).

Writing linear equations in all forms (video) | Khan Academy