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Slope-intercept equation from slope & point

Learn how to write an equation in slope-intercept form (y=mx+b) for the line with a slope of -3/4 that goes through the point (0,8). We identify the slope (m) and y-intercept (b) to create our equation y = (-3/4)*x + 8. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • leaf green style avatar for user Jin Hee Kim
    i fully understand that y=mx+b works when you are tryig to find out the y
    but i do not understand why you have to +b
    can someone please tell me why is that?
    (93 votes)
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  • mr pink red style avatar for user Callum Bertolini
    I made my own equation:

    (2,3) & (6,9)

    thus:
    9-3/6-2= 6/4 OR 1.5

    Which equaled y=1.5x + b

    I used 2-3 to make it
    3=1.5(2)+b 3 being y 1.5 being M and (2) being X
    which makes > 3=3+b


    now when i put 3 on both sides of my equation, both 3's cancel out. Does this make b=0 OR do i have to use (6,9) instead of (2,3) OR is there no b?

    ~Callum :-)
    (17 votes)
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  • duskpin ultimate style avatar for user christine
    why is it that there's an y-int but not a x-int??
    (11 votes)
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  • blobby green style avatar for user Michelle
    I thought that the slope was canceled out because of the zero, which changed the equation to y=b? I understand that the zero cancels itself out when multiplied but I dont understand why the "mx" came back after being canceled. Help me please
    (7 votes)
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    • male robot hal style avatar for user Aviral Goel
      the 'mx' only got canceled when we assumed the value of x=0 but as we move along the line the value of 'x' changes hence, mx comes back.
      What I mean is
      We know, y = mx + b
      If x = 0, y=b, but since value of x may change we write the equation back in standard form
      y=mx + b
      (7 votes)
  • piceratops ultimate style avatar for user Jacob
    This is more of an order of operations question than anything else, but can someone explain to me "why" it would be improper to isolate the b and then make it positive before doing anything else? Please don't just say you wont get the correct answer if you don't do it correctly, I want you to explain how this is violating the order of operations and other cross equation simplifications are not violating those principles...

    This is a screenshot of what the program says is the proper sequence:

    https://drive.google.com/file/d/0B0a8mT2yOILSRTNkNkJESEpDZDg/view?usp=sharing

    This is a picture of the sequencing I'm confused about being wrong:

    https://drive.google.com/file/d/0B0a8mT2yOILSdkEzdEhqbjBncE0/view?usp=sharing
    (4 votes)
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    • spunky sam blue style avatar for user stephen.broughton2
      In this step:
      -b = (-13/6) (13) + 26,
      b = (13/6) (-13) - 26
      you've made a mistake. You distributed a negative to both m and x when they should get only a single negative between them. Essentially, you're saying that

      -z = xy is the same as z = (-x)(-y), which is only true when z = 0.

      Distributing the negative properly gives you
      b = (13/6) (13) - 26 = 169/6 - 174/6 = -5/6,
      as expected.
      (6 votes)
  • blobby green style avatar for user LUCAM
    remember that there's people who commented here that are now fully grown up
    (6 votes)
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  • blobby green style avatar for user Erin Rhoades
    I have to write an equation in Slope intercept form y=mx+b
    I have a slope of 3 and an x intercept of 2.
    How do I solve that without a y intercept/
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      The 1st response you received is incorrect. This is doable.
      As you have already notices, we don't have the y-intercept. So, we need to calculate it. Remember, "b" in the form: "y=mx+b" is the y-intercept. We're going to use this formula and calculate "b". We have a value we can use for all the other variables: y = 0 (from x-intercept); x = 2 (from x-intercept) and m = 3. Substitute and calculate "b".
      0 = 3(2) + b
      0 = 6 + b
      -6 = b

      Now, we can create the equation of the line using slope of 3 and y-intercept of -6
      y = 3x - 6
      Hope this helps.
      (6 votes)
  • blobby green style avatar for user lexahope101
    how would you find x or y in an equation for slope?
    (2 votes)
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    • starky ultimate style avatar for user DJBB
      If you are talking about the y value for a given x value, you should just use the slope-intercept form and solve it algebraically. For an example, let's say that x = 8.

      Using the slope-intercept form of the equation in the video, y = -3/4x+8. We can substitute 8 for x, which gives us y = -3/4(8)+8. The right hand side of the equation can be simplified by multiplying -3/4 * 8, then adding 8. This gives you 2. Therefore the equation now reads y = 2.

      I only used 8 as an example for an x value here, but you can use any value you want.
      (6 votes)
  • blobby green style avatar for user Gayathri  Prakash
    How come when you use a different coordinate to find b I am getting a different answer?
    (4 votes)
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    • stelly blue style avatar for user Kim Seidel
      Any point on the line with the slope can be used to find the value of "b". It is always the same number. If you got a different result using a different point, then you have a math error. Without a specific example and your work, i can't tell what you did wrong.
      (1 vote)
  • aqualine ultimate style avatar for user i cant code lol
    what do you do when the x coordinate is an actual number, not zero
    (3 votes)
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Video transcript

A line has a slope of negative 3/4 and goes through the point 0 comma 8. What is the equation of this line in slope-intercept form? So any line can be represented in slope-intercept form, is y is equal to mx plus b, where this m right over here, that is of the slope of the line. And this b over here, this is the y-intercept of the line. Let me draw a quick line here just so that we can visualize that a little bit. So that is my y-axis. And then that is my x-axis. And let me draw a line. And since our line here has a negative slope, I'll draw a downward sloping line. So let's say our line looks something like that. So hopefully, we're a little familiar with the slope already. The slope essentially tells us, look, start at some point on the line, and go to some other point of the line, measure how much you had to move in the x direction, that is your run, and then measure how much you had to move in the y direction, that is your rise. And our slope is equal to rise over run. And you can see over here, we'd be downward sloping. Because if you move in the positive x direction, we have to go down. If our run is positive, our rise here is negative. So this would be a negative over a positive, it would give you a negative number. That makes sense, because we're downward sloping. The more we go down in this situation, for every step we move to the right, the more downward sloping will be, the more of a negative slope we'll have. So that's slope right over here. The y-intercept just tells us where we intercept the y-axis. So the y-intercept, this point right over here, this is where the line intersects with the y-axis. This will be the point 0 comma b. And this actually just falls straight out of this equation. When x is equal to 0-- so let's evaluate this equation, when x is equal to 0. y will be equal to m times 0 plus b. Well, anything times 0 is 0. So y is equal to 0 plus b, or y will be equal to b, when x is equal to 0. So this is the point 0 comma b. Now, they tell us what the slope of this line is. They tell us a line has a slope of negative 3/4. So we know that our slope is negative 3/4, and they tell us that the line goes through the point 0 comma 8. They tell us we go through the-- Let me just, in a new color. I've already used orange, let me use this green color. They tell us what we go through the point 0 comma 8. Notice, x is 0. So we're on the y-axis. When x is 0, we're on the y-axis. So this is our y-intercept. So b, we could say-- we could do a couple-- our y-intercept is the point 0 comma 8, or we could say that b-- Remember, it's also 0 comma b. We could say b is equal to 8. So we know m is equal to negative 3/4, b is equal to 8, so we can write the equation of this line in slope-intercept form. It's y is equal to negative 3/4 times x plus b, plus 8. And we are done.