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Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

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Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

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Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

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Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

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Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

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Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

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- [Sal] Let's do some practice examples from our intro to slope y intercept exercise. What is the slope of y is equal to negative four x minus three? So you might already recognize, this is in slope intercept form. Just as a reminder, slope intercept form is y is equal to mx plus b, where the coefficient on this x term right over here, that is our slope, and then this constant right over here, that is going to give you your y intercept. So if they're saying, what is the slope here? Well I just need to figure out, what is the coefficient on this x term? And you can see that the coefficient here is a negative four. So that is going to be our m, that is going to be our slope. Now just as a reminder, you have to make sure that it's solved in this way, that is is solved for y, y is equal to something times x minus three, so that's our slope. Let's do another one of these. So we're asked, what is the y intercept of y is equal to negative three x minus two? So once again we already have it in slope intercept form. It's already been solved for y. It's of the form y is equal to mx plus b, where m, our slope, is given right over here, negative three. But they're not asking for our slope, they're asking for the y intercept. Well the y intercept is given by b here, so b is negative two. Pay close attention to the sign here. So b is equal to negative two. But when I look at these choices, I don't see a b is equal to negative two, so what are they talking about? Well a y intercept is, what is the y value when x is equal to zero? And you could see that here, if x was equal to zero then that term goes away and y is equal to b. So if you want to know the point where the graph described by this equation intercepts the y axis, well it's going to be what is y when x is equal to zero? Well when x is equal to zero, y is equal to negative two. And you could see that in our original equation, again. If x were zero, this term would go away, and y would be equal to negative two. So zero, comma, negative two. So it would be that choice right over there. On Khan Academy obviously you just have to click on that, you don't have to shade it in. Let's do one more. Complete the equation of the line whose slope is five, and y intercept is zero, comma, four. So once again the general form is y is equal to our slope times x, if I want to put it in slope intercept form, plus our y intercept. Well they're telling us, our slope is five. Whose slope is five. So we know that m is going to be five. And they tell us that the y intercept is zero, four. So the y intercept, b, that is the value of y when x is equal to zero. So the value of y when x equals zero is this four right over here. So that is going to be four. So I could say y is equal to five times x plus four. And when you're actually entering it on Khan Academy, you would just type it in, or if you're using the app you would use it with your finger. And I always make the mistake of writing y equals, and I type in y equals five x plus four. Notice they already gave you the y equals right over there. That's all you have to do, recognize the slope, the y intercept, and then remember what the slope intercept form actually is.

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Worked examples: slope-intercept intro (video) | Khan Academy

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Sal] Let's do some practice examples from our intro to slope y intercept exercise. What is the slope of y is equal to negative four x minus three? So you might already recognize, this is in slope intercept form.

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Topics

Description

Explore slope-intercept form of a line. Connect the slope and y-intercept to the equation of the line. Challenge yourself in the line game!

Sample Learning Goals

Graph a line given an equation in slope-intercept form.

Write an equation in slope-intercept form given a graphed line.

Predict how changing the values in a linear equation will affect the graphed line.

Predict how changing the graphed line will affect the equation.

Standards Alignment

Common Core - Math

8.EE.B.6 8.EE.C.8a 8.EE.C.8b 8.F.A.3

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Teacher Tips

Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Video Primer

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Teacher-Submitted Activities

The new HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 12+ Safari
iPad compatible sims

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge and Internet Explorer 11, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.9.5+, Safari 9+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

# data[].attributes.attachment_link.description
Explore slope-intercept form of a line. Connect the slope and y-intercept to the equation of the line. Challenge yourself in the line game!

# data[].attributes.attachment_link.description
Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

# data[].attributes.attachment_link.description
Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

# data[].attributes.attachment_link.description
Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.

# data[].attributes.attachment_link.description
Explained using the cloud collaboration platform built on the learning technology of tomorrow - Explain Everything.