When is slope intercept form used

There are two big benefits that result when you put an equation in slope-intercept form and you can probably figure out what they are based on the name : You can identify the slope and y -intercept of the line get this without doing any additional work at all!

Plus, if you transform equations while you do sit-ups, the slope-intercept form could actually give you greater definition in your abs! Let's get mathematical for a moment. Officially speaking, the slope-intercept form of a line is written like this:.

The coefficient of the x term, m , is the slope of the line and the number or constant , b , is the y -intercept. In other words, once you solve a linear equation for y , the coefficient of x will be the slope of the line, and the number with no variable attached called the constant marks the spot on the y -axis, 0, b , where the line passes through. So if you took two different points on this line, you would still get that the slope is 1 1 1.

You may know what the slope intercept form looks like, but half the time you will be given equations that are not in that form. So it is your job to turn it into slope-intercept form. How do we do that? The goal is to always isolate the y y y term. For example, let's say you're given the equation. Now the 2 2 2 is in the way of y y y , so we are going to get rid of it by dividing both sides of the equation by 2 2 2. Now that we know the y intercept and slope really well, why don't we look at specific questions about finding them!

We just need to find out what b b b is. Now this linear equation is not in slope intercept form, so we have to change it into that form first. Our goal is to isolate y y y in this equation. See that if we move the 2 x 2x 2 x to the right side of equation, we will have:. Let's do another similar question. This may look a bit weird because there is no x x x term, but our goal remains the same. We are going to isolate y y y. Dividing both sides of the equation by 4 4 4 gives us.

Now this may not look like it, but the equation is in slope intercept form. Just rewrite the equation as. Let's do one more question.

This one is interesting because the equation has no y y y term. So how are we supposed to put it in slope intercept form? Well, the only thing we can do right now is isolate for x x x , so let's try that for now.

Moving the 15 15 15 to the right hand side of equation we have:. Now we are going to draw this on a graph. Notice that in this equation, x x x is forced to be 3 3 3 and cannot be anything else. However, it doesn't say anything about y y y , so y y y can be anything it likes. If we were to write a table of values, we get:.

If we plot these points on a coordinate plane and draw the line, we have:. Notice how the line never touches the y-axis. This means the equation does not have a y intercept.

Now that we covered all the cases of finding the y intercept, let's look at questions which ask us to find the slope! As you can see, the equation is not in slope intercept form, so we have to convert it into that form first. Our goal is to isolate y y y. Moving 6 x 6x 6 x to the right side of the equation gives:. So we can rewrite the equation to:. Since m m m is the slope, then the slope must be 1 1 1. Let's do a slightly harder one. Again, this is a little weird because we have no x x x term.

However, our goal to isolate y y y stays the same. Dividing both sides of the equation by 2 2 2 gives:. So we can rewrite our equation as:.

If you are wondering what a line with 0 0 0 slope looks like, then here is a graph for you to see. What is the slope intercept form of the line pictured in the graph below?

A line with a slope of 2 and a y-intercept of A line with a slope of 3 and a y-intercept of Popular pages mathwarehouse. Surface area of a Cylinder. Unit Circle Game. Pascal's Triangle demonstration. Create, save share charts. Interactive simulation the most controversial math riddle ever! Calculus Gifs. How to make an ellipse. The main difficulty is usually in interpreting the horizontal variable, especially when that variable is keyed to a certain year.

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