Linear functions slope-intercept form write an equation in slope

The slope intercept form calculator will help you find the equation of a line if you know two points it goes through. Read more… The slope intercept form calculator tells you how to find the equation of a line for any given two points that this line passes through.

Slope-intercept form linear equations Video transcript - [Voiceover] There's a lot of different ways that you could represent a linear equation. So for example, if you had the linear equation y is equal to 2x plus three, that's one way to represent it, but I could represent this in an infinite number of ways.

I could, let's see, I could subtract 2x from both sides, I could write this as negative 2x plus y is equal to three. I could manipulate it in ways where I get it to, and I'm gonna do it right now, but this is another way of writing that same thing.

You could actually simplify this and you could get either this equation here or that equation up on top. These are all equivalent, you can get from one to the other with logical algebraic operations. So there's an infinite number of ways to represent a given linear equation, but I what I wanna focus on in this video is this representation in particular, because this one is a very useful representation of a linear equation and we'll see in future videos, this one and this one can also be useful, depending on what you are looking for, but we're gonna focus on this one, and this one right over here is often called slope-intercept form.

And hopefully in a few minutes, it will be obvious why it called slop-intercept form. And before I explain that to you, let's just try to graph this thing. I'm gonna try to graph it, I'm just gonna plot some points here, so x comma y, and I'm gonna pick some x values where it's easy to calculate the y values.

So maybe the easiest is if x is equal to zero. If x is equal to zero, then two times zero is zero, that term goes away, and you're only left with this term right over here, y is equal to three. Y is equal to three.

And so if we were to plot this. Actually let me start plotting it, so that is my y axis, and let me do the x axis, so that can be my x, oh that's not as straight as I would like it.

So that looks pretty good, alright. That is my x axis and let me mark off some hash marks here, so this is x equals one, x equals two, x equals three, this is y equals one, y equals two, y equals three, and obviously I could keep going and keep going, this would be y is equal to negative one, this would be x is equal to negative one, negative two, negative three, so on and so forth.

So this point right over here, zero comma three, this is x is zero, y is three. Well, the point that represents when x is equal to zero and y equals three, this is, we're right on the y axis.

If they have a line going through it and this line contains this point, this is going to be the y- intercept. So one way to think about it, the reason why this is called slope-intercept form is it's very easy to calculate the y-intercept. The y-intercept here is going to happen when it's written in this form, it's going to happen when x is equal to zero and y is equal to three, it's gonna be this point right over here.

So it's very easy to figure out the intercept, the y-intercept from this form. Now you might be saying, well it says slope-intercept form, it must also be easy to figure out the slope from this form.

And if you made that conclusion, you would be correct! And we're about to see that in a few seconds. So let's plot some more points here and I'm just gonna keep increasing x by one. So if you increase x by one, so we could write that our delta x, our change in x, delta Greek letter, this triangle is a Greek letter, delta, represents change in.

Change in x here is one. We just increased x by one, what's gonna be our corresponding change in y? What's going to be our change in y? So let's see, when x is equal to one, we have two times one, plus three is going to be five.

So our change in y is going to be two. Let's do that again.Equation of a line in slope intercept form, as well as how to find equation given slope and one point.

Includes you-tube video Lesson with pictures and many example problems. Write the slope intercept form for the lines below. Problem 5. A line with a slope of 2 and a y-intercept of interactive linear equation ; equation given slope. The slope intercept form is probably the most frequently used way to express equation of a line.

Writing Linear Equations Date_____ Period____ Write the slope-intercept form of the equation of each line. 1) 3 x − 2y = −16 2) 13 x − 11 y = −12 3) 9x Write the point-slope form of the equation of the line described. 17) through: (4, 2), parallel to y. Section Graphing Linear Equations in Slope-Intercept Form EEssential Questionssential Question How can you describe the graph of the equation y = mx + b? Slope is the rate of change between any two points on a line. It is the measure of the steepness of the line. To fi nd the slope of a line, fi nd the ratio of the. Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.

To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line. Linear Functions: Slope-Intercept Form Teacher Notes Objectives • To review the form of the equation y = mx + b, where m is slope and b is the y-intercept.

Slope Intercept Equation of Vertical and Horizontal lines Vertical Lines. The Equation of a vertical line is x = b. Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same.

Therefore, whatever the x value is, is also the value of 'b'. Linear Equations in Slope Intercept Form. Home > Printable Resources > Math Worksheets > Slope Intercept Form; Write the linear equation that defines the relationship between the X and Y values in the form y = mx + b. Slope Intercept Form; Slope of a Line; Worksheets.

Perpendicular Lines

Equation of a Line - Determining and Plotting. Algebra I is an entirely new course designed to meet the concerns of both students and their parents. These 36 accessible lectures make the concepts of first-year algebra - including variables, order of operations, and functions-easy to grasp.