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Slope-intercept equation from slope & point (old)

An old video where Sal finds the slope-intercept form of a line that has a slope of 7 and goes through the point (-4,-11). Created by Sal Khan and Monterey Institute for Technology and Education.

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  • leaf yellow style avatar for user Mo
    Doesn't the steepness of a slope depend on the marginal value of units on a given graph? So the steepness of a slope of (7) could be very steep (if numbered by units of one) or not steep at all (if numbered by units of 100). (I believe advertisers use this trick to fool people on rises and falls of certain markets)
    (15 votes)
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    • hopper cool style avatar for user Chuck Towle
      Mo,
      The steepness would be the same no matter which units you use.
      If you used units of 100, you would go over 100 and up 700.
      In you used units of 1/10, you would go over 1/10 and up 7/10.

      In fact, if the line goes through the origin, the points (1/10 , 7/10) and (100,700) would both be on the line. The steepness of the line would be a slope of 7.
      The steepness of the line would be the exact same.

      But, yes, advertisers and others do often use math misconceptions to mislead people.
      (20 votes)
  • aqualine ultimate style avatar for user Fatin Iftekhar
    What is the m and what is the b in y=mx+b?
    (5 votes)
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  • duskpin ultimate style avatar for user Amogh Mandava
    How does a linear equation become undefined. Can it go on forever, and can it be negative? Also, why is the y-axis undefined, but the x-axis is different. What is the reason behind that?
    (5 votes)
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    • leafers ultimate style avatar for user --  .-  .-.  - .  .-..  Leafer
      Hi Amogh Mandava!

      When finding the slope of a line using the slope formula (y2-y1/x2-x1), the slope of a vertical line would be (y/0). However, division by zero is undefined. Hence, the equation's slope is undefined. However, for a horizontal line, the slope formula would end up (0/x). A number divided by zero is zero. Thus, we can determine that a horizontal line's slope is 0.
      slr
      (1 vote)
  • aqualine ultimate style avatar for user Cutepinky
    So the answer to this question would be in equation form? And all we have to figure out is m and b, right?
    (4 votes)
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  • leafers seed style avatar for user Nina Rakic
    Hey! I haven't practiced math in over ten years and am now preparing for the GMAT. Your videos have been invaluable in the refreshing process: my memory thanks you. Actually, I have a number of friends that are currently preparing for the GMAT and they all use your videos. Keep it up!
    (5 votes)
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  • piceratops ultimate style avatar for user blmartin4295
    why couldn't a vertical line have a equation something like y=(ifinity/0)x+0 which I know a number divided by 0 is undefined I was just wandering if this would define a vertical line with an equation
    (1 vote)
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    • blobby green style avatar for user Creeksider
      The problem isn't coming up with an equation. For example, the equation of a vertical line through the point (3,0) is x=3. The problem is that the slope of the line is undefined, because we get zero in the denominator of a fraction. It's natural to feel there's something unsatisfactory in this state of affairs and wonder if there might be some way around it, but in the end it's just a fact of life we have to accept.
      (3 votes)
  • leafers ultimate style avatar for user obviouslynotagolfer
    Is the equation y=mx+b interchangeable with x=my+b with "b" as the x intercept?
    (1 vote)
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  • starky tree style avatar for user MarcaidaRoss
    How Would We Solve y=mx-2
    (1 vote)
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    • blobby green style avatar for user Aidan Fleming
      This is the equation of a line on a graph, to solve this you must realise, the equation can also be written as 1y=1m1x-2. Y= The location of the point on the Y axis. X= The location of the point on the X axis. M= The slope. -2= Is the Y intercept, If there is a graph you can replace X and Y with the real co-ordinates, Ex: X=3 Y=5 5=3x-2. I hope it helps, that's how I'd solve it. :D
      (3 votes)
  • blobby green style avatar for user garlynmercy
    line t is perpendicular to line y=4x. what is the gradient of line t
    (1 vote)
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  • blobby green style avatar for user garlynmercy
    find the equation of a line that passes through (-6,3) and (2,5)
    (1 vote)
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Video transcript

A line has a slope of 7 and goes through the point negative 4, negative 11. What is the equation of this line in slope-intercept form? So the equation of any line in slope-intercept form is y is equal to mx plus b, where m is the slope and b is the y-intercept. Now, in this problem right here, they tell us the slope. They tell us that a line has a slope of 7. So we know right from the get go that m is equal to 7. So we know the equation of this line in slope-intercept form is going to look like y is equal to, we know m is 7, so 7x plus-- let me make that x a little bit neater-- 7x plus b. And now what we need to do, we need to figure out b, and they give us one more piece of information. They say that the line goes through the point negative 4 comma negative 11. So that tells us that when x is equal to negative 4, then y is equal to negative 11. So we can use this information in what we have or the part of our equation that we've been able to figure out so far. We know that when x is equal to negative 4, y is going to be equal to negative 11. So what b do we need to make that happen? Let's try it out. So y is negative 11 when x is equal to negative 4. So negative 11 is equal to 7 times x-- and in this case x is negative 4-- plus b. And now we can just solve for b. A b that makes this equation, or that satisfies the constraint that when x is equal to negative 4, y is equal to negative 11. So let's see, we get negative 11 is equal to 7 times negative 4 is negative 28 plus b, and now we can add a 28 to both sides of this equation. So let's add a 28. I'm just trying to isolate the b on the right-hand side. And so on the left-hand side, negative 11 plus 28, that is just positive 17. These guys cancel out on purpose. And I just have a b on the right-hand side. So I get b is equal to 17. Let me write it in green. That's not green. We get b is equal to 17. So we know m is 7, they told us that right at the beginning. And now we know b is 17. So the equation of our line is y is equal to 7x, that's our slope. 7 times x plus b, and b here is 17. And if we wanted to graph it, it would look something like this. I'll just do a real rough graph. So if we wanted to graph this line, that's my x-axis, and this is my y-axis. The y-intercept is 17. So that means that the point 0, 17 is on this line. So this point right over here is going to be 0, 17. And our slope is 7. So that means if we move to the right one, we move up t seven. So it's a high slope. So if we move to the right one, we move up seven. Or if we move back one, will move down seven. So we'll move down seven, so the line will look roughly like this. Obviously, haven't done it very exactly, but our line is going to look like. That's going to be a pretty steep upward-sloping line. It has a very high slope, slope of seven. If you move one in the x direction, you have to move up seven. And its y-intercept is at y is 17. When x is 0, y is 17.