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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. 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. 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.
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.Salle, your equation y = (5/4)x + 3 is in slope-intercept form.
The slope or m is 5/4 and the y-intercept or b is 3. You have already shown if x = 0, then y = 3. Writing Linear Equations Given Slope and a Point. When you are given a real world problem that must be solved, you could be given numerous aspects of the equation.
If you are given slope and the y-intercept, then you have it made. You have all the information you need, and you can create your graph or write an equation in slope intercept form very easily.
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. The rise over run of the line. Or the inclination of the line.
And b is the y-intercept. An algebraic equation in which each element (or term) is either a constant or the product of the first power of a single variable and a constant is called a linear equation.
These equations can have one or more variables. Depending on the number of variables (we will mark that number with the letter n), a linear equation is the algebraic representation of a straight line in a coordinate system. kcc1 Count to by ones and by tens. kcc2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
kcc3 Write numbers from 0 to Represent a number of objects with a written numeral (with 0 representing a count of no objects). kcc4a When counting objects, say the number names in the standard order, pairing each object with one and only.
Several questions on the GED math test will require you to understand and know how to work with fractions. Fractions are normally used to express parts of a whole number.