Linear functions slope-intercept form write an equation from a graph

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Linear functions slope-intercept form write an equation from a graph

Slope-intercept form linear equations Video transcript So you may or may not already know that any linear equation can be written in the form y is equal to mx plus b. Where m is the slope of the line. The same slope that we've been dealing with the last few videos.

linear functions slope-intercept form write an equation from a graph

The rise over run of the line. Or the inclination of the line. And b is the y-intercept. I think it's pretty easy to verify that b is a y-intercept.

linear functions slope-intercept form write an equation from a graph

The way you verify that is you substitute x is equal to 0. If you get x is equal to remember x is equal to 0, that means that's where we're going to intercept at the y-axis. If x is equal to 0, this equation becomes y is equal to m times 0 plus b.

I don't care what m is.

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So then y is going to be equal to b. So the point 0, b is going to be on that line. The line will intercept the y-axis at the point y is equal to b. We'll see that with actual numbers in the next few videos.

Just to verify for you that m is really the slope, let's just try some numbers out. We know the point 0, b is on the line. What happens when x is equal to 1? You get y is equal to m times 1. Or it's equal to m plus b. So we also know that the point 1, m plus b is also on the line. This is just the y value.

So what's the slope between that point and that point? Let's take this as the end point, so you have m plus b, our change in y, m plus b minus b over our change in x, over 1 minus 0. This is our change in y over change in x. We're using two points.

That's our end point. That's our starting point. So if you simplify this, b minus b is 0. So hopefully you're satisfied and hopefully I didn't confuse you by stating it in the abstract with all of these variables here.

But this is definitely going to be the slope and this is definitely going to be the y-intercept. Now given that, what I want to do in this exercise is look at these graphs and then use the already drawn graphs to figure out the equation.

So we're going to look at these, figure out the slopes, figure out the y-intercepts and then know the equation. So let's do this line A first.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. General Equation of a Line: ax + by = c. Explore the graph of the general linear equation in two variables that has the form ax + by = c using an applet.

Using slope intercept form is one of the quickest and easiest ways to graph a linear equation. Before we begin, I need to introduce a little vocabulary.

Converting Equations to the Slope-Intercept Formula. Let’s say we are given an equation in a form other than \(\boldsymbol{y=mx+b}\) and we were asked to graph’s graph the line: \(x=7y+3\) We know that this equation is not in the slope-intercept form, and we must use what we’ve learned about algebra to somehow get it in the form we know.

Graphing a Linear Equation Using Slope Intercept Form. Now that you've completed a lesson on graphing slope you are finally ready to graph linear equations..

Writing slope-intercept equations

There are several different ways to graph linear equations. You've already learned how to graph using a table of's okay for the beginner, but it can be a little time consuming. Aug 15,  · This algebra video review tutorial shows you how to graph a linear equation in slope intercept form y=mx+b and standard form ax+by=c.

This video is for high school students taking algebra 1 .

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