Equation of a line
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Graphing a line in slope intercept form
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Converting to slope-intercept form
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Graphing linear equations
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Linear Equations in Slope Intercept Form
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Graphs Using Slope-Intercept Form
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Word Problem Solving 4
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Equation of a line 1
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Equation of a line 2
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Equation of a line 3
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Solving for the y-intercept
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Slope intercept form
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Linear Equations in Point Slope Form
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Point slope form
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Linear Equations in Standard Form
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Point-slope and standard form
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Converting between slope-intercept and standard form
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Converting between point-slope and slope-intercept
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Finding the equation of a line
Point-slope and standard form Point-slope and standard form
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- A line passes through the points negative 3, 6 and 6, 0.
- Find the equation of this line in point slope form, slope
- intercept form, standard form.
- And the way to think about these, these are just three
- different ways of writing the same equation.
- So if you give me one of them, we can manipulate it to get
- any of the other ones.
- But just so you know what these are, point slope form,
- let's say the point x1, y1 are, let's say that that is a
- point on the line.
- And when someone puts this little subscript here, so if
- they just write an x, that means we're talking about a
- variable that can take on any value.
- If someone writes x with a subscript 1 and a y with a
- subscript 1, that's like saying a particular value x
- and a particular value of y, or a particular coordinate.
- And you'll see that when we do the example.
- But point slope form says that, look, if I know a
- particular point, and if I know the slope of the line,
- then putting that line in point slope form would be y
- minus y1 is equal to m times x minus x1.
- So, for example, and we'll do that in this video, if the
- point negative 3 comma 6 is on the line, then we'd say y
- minus 6 is equal to m times x minus negative 3, so it'll end
- up becoming x plus 3.
- So this is a particular x, and a particular y.
- It could be a negative 3 and 6.
- So that's point slope form.
- Slope intercept form is y is equal to mx plus b, where once
- again m is the slope, b is the y-intercept-- where does the
- line intersect the y-axis-- what value does y take
- on when x is 0?
- And then standard form is the form ax plus by is equal to c,
- where these are just two numbers, essentially.
- They really don't have any interpretation
- directly on the graph.
- So let's do this, let's figure out all of these forms. So the
- first thing we want to do is figure out the slope.
- Once we figure out the slope, then point slope form is
- actually very, very, very straightforward to calculate.
- So, just to remind ourselves, slope, which is equal to m,
- which is going to be equal to the change in y over the
- change in x.
- Now what is the change in y?
- If we view this as our end point, if we imagine that we
- are going from here to that point, what is
- the change in y?
- Well, we have our end point, which is 0, y ends up at the
- 0, and y was at 6.
- So, our finishing y point is 0, our starting y point is 6.
- What was our finishing x point, or x-coordinate?
- Our finishing x-coordinate was 6.
- Let me make this very clear, I don't want to confuse you.
- So this 0, we have that 0, that is that 0 right there.
- And then we have this 6, which was our starting y point, that
- is that 6 right there.
- And then we want our finishing x value-- that is that 6 right
- there, or that 6 right there-- and we want to subtract from
- that our starting x value.
- Well, our starting x value is that right over there, that's
- that negative 3.
- And just to make sure we know what we're doing, this
- negative 3 is that negative 3, right there.
- I'm just saying, if we go from that point to that point, our
- y went down by 6, right?
- We went from 6 to 0.
- Our y went down by 6.
- So we get 0 minus 6 is negative 6.
- That makes sense.
- Y went down by 6.
- And, if we went from that point to that point, what
- happened to x?
- We went from negative 3 to 6, it should go up by 9.
- And if you calculate this, take your 6 minus negative 3,
- that's the same thing as 6 plus 3, that is 9.
- And what is negative 6/9?
- Well, if you simplify it, it is negative 2/3.
- You divide the numerator and the denominator by 3.
- So that is our slope, negative 2/3.
- So we're pretty much ready to use point slope form.
- We have a point, we could pick one of these points, I'll just
- go with the negative 3, 6.
- And we have our slope.
- So let's put it in point slope form.
- All we have to do is we say y minus-- now we could have
- taken either of these points, I'll take this one-- so y
- minus the y value over here, so y minus 6 is equal to our
- slope, which is negative 2/3 times x minus our
- x-coordinate.
- Well, our x-coordinate, so x minus our x-coordinate is
- negative 3, x minus negative 3, and we're done.
- We can simplify it a little bit.
- This becomes y minus 6 is equal to negative 2/3 times x.
- x minus negative 3 is the same thing as x plus 3.
- This is our point slope form.
- Now, we can literally just algebraically manipulate this
- guy right here to put it into our slope intercept form.
- Let's do that.
- So let's do slope intercept in orange.
- So we have slope intercept.
- So what can we do here to simplify this?
- Well, we can multiply out the negative 2/3, so you get y
- minus 6 is equal to-- I'm just distributing the negative
- 2/3-- so negative 2/3 times x is negative 2/3 x.
- And then negative 2/3 times 3 is negative 2.
- And now to get it in slope intercept form, we just have
- to add the 6 to both sides so we get rid of it on the
- left-hand side, so let's add 6 to both
- sides of this equation.
- Left-hand side of the equation, we're just left with
- a y, these guys cancel out.
- You get a y is equal to negative 2/3 x.
- Negative 2 plus 6 is plus 4.
- So there you have it, that is our slope intercept form, mx
- plus b, that's our y-intercept.
- Now the last thing we need to do is get it into
- the standard form.
- So once again, we just have to algebraically manipulate it so
- that the x's and the y's are both on
- this side of the equation.
- So let's just add 2/3 x to both sides of this equation.
- So I'll start it here.
- So we have y is equal to negative 2/3 x plus 4, that's
- slope intercept form.
- Let's added 2/3 x, so plus 2/3 x to both
- sides of this equation.
- I'm doing that so it I don't have this 2/3 x on the
- right-hand side, this negative 2/3 x.
- So the left-hand side of the equation-- I scrunched it up a
- little bit, maybe more than I should have-- the left-hand
- side of this equation is what?
- It is 2/3 x, because 2 over 3x, plus this y, that's my
- left-hand side, is equal to-- these guys cancel out-- is
- equal to 4.
- So this, by itself, we are in standard form, this is the
- standard form of the equation.
- If we want it to look, make it look extra clean and have no
- fractions here, we could multiply both sides of this
- equation by 3.
- If we do that, what do we get?
- 2/3 x times 3 is just 2x.
- y times 3 is 3y.
- And then 4 times 3 is 12.
- These are the same equations, I just multiplied
- every term by 3.
- If you do it to the left-hand side, you can do to the
- right-hand side-- or you have to do to the right-hand side--
- and we are in standard form.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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