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Slope & direction of a line

Sal graphs a line that has a slope that is negative and greater than the slope of another line. Created by Sal Khan.

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  • aqualine ultimate style avatar for user Randall Pellman
    how do you know if its a positive or negative slope?
    (41 votes)
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  • duskpin ultimate style avatar for user Michelle Yoon
    At , it is mentioned that the orange line has to have a slope greater than the slope of the blue line. I thought if a line's slope needs to be greater, it would be more negative, or have a steeper slope, shown at . However, the video makes the blue line's slope steeper than the orange line's. Why and how?
    Thanks!
    (30 votes)
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    • female robot grace style avatar for user adeelnkhan
      I think the confusion is related to how the video ends. Because the question asks for 'slope greater than the blue line'. But the video ends on the slope being categorized as < the slope of the blue line and then the answer is checked.

      The presenter, Sal, was trying to categorize the different ways that the slope can be represented (Positive, negative or zero). Maybe, the presenter should have categorized the different ways and then left the ending of the video by categorizing a slope that was indeed steeper/more negative, compared to the blue line.
      (3 votes)
  • piceratops tree style avatar for user russell.spencer
    I'm confused with the undefined slope
    (5 votes)
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    • hopper cool style avatar for user Chuck Towle
      Russell,
      If you have a vertical line,
      then the x value remains the same.
      The change in x is always 0.

      For instance of a line is vertical and crosses the x axis at 1,
      the point (1,0), (1,2), (1,8) would all be on the line.

      Slope is (change in y)/(change in x).
      But the (change in x) is always 0 for a vertical line.
      So the slope is something divided by 0 which is undefined.

      For instance it you take the points (1,2) and (1,0),
      then the slope is (2-0)/(0-0) = 2/0
      But anything divided by 0 is undefined.
      So the slope of a vertical line is also undefined.

      When the slope is "undefined" then that defines the line as vertical.
      The slope is undefined, but the line is defined.

      The equation of a vertical line is x=0 or x=1 or x=some constant.

      If written with a y in the equation,
      x=1 becomes
      x + 0y =1
      This cannot be converted to slope y-intercept form, because you cannot isolate a 1y by itself on one side of the equation. It also has no defined slope and it never crosses the y axis, so it has no y-intercept.

      x=1 or x+0y = 1 also cannot be converted to point-slope form. It just cannot be done. And one of the reasons is that the slope is undefined.

      I hope something I said helps make it click for you.
      (20 votes)
  • aqualine tree style avatar for user Daniel Brown
    In the UK we call slope the Gradient.
    (9 votes)
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  • purple pi teal style avatar for user Tanisha
    What is an undefined slope?
    (6 votes)
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  • piceratops tree style avatar for user Justin Chu
    So if the line is horizontal, the slope is zero, right? So what would be the slope of a line that is vertical?
    (3 votes)
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  • blobby green style avatar for user Reginald Tang
    what happens if Sal flipped the line upside-down?
    will X become Y & Y become X?
    (3 votes)
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  • blobby green style avatar for user Filipe Pinto
    Can anyone tell me how is one slope greater than another?
    (2 votes)
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  • starky ultimate style avatar for user Md Abu Qatadah Farooqui
    how to calculate the slope of a line drawn simply on a graph?and what does Y (the one we are changing so as to get the line meet the two dots) mean in our practice tests?
    I really need help with this matter.really weak in slope intuition. Thanks!
    (2 votes)
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  • purple pi teal style avatar for user Ilina
    If you had a line that was vertical, would it have a positive slope?
    (2 votes)
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    • piceratops ultimate style avatar for user Steven Donald
      No, if the line is vertical then the slope is undefined. The slope is the measure of the rise (or change in the y-axis) over the run (or change in the x-axis). Since a vertical line has no change in x-axis, or rather, all points share the same x-value, it would have 0 for denominator, which makes the fraction, and thus the slope, undefined.
      (2 votes)

Video transcript

Graph a line that has a slope that is negative and greater than the slope of the blue line. So let's think for a second about what slope means. So if you use the word slope in your everyday life, you're really talking about how inclined something is, like a ski slope. So for example, this orange line isn't inclined at all. It's flat, so this one actually has a slope of 0. Another way of thinking about it is as x increases, what is happening to y? And you see here that y isn't changing at all, so this orange line right now has a slope of 0. If the orange line looked like this, it now has a positive slope. Notice, when x is negative, your y value-- or say when x is negative 5, your y value is here, and then when x is positive 5, your y value has increased. As x increases, y is increasing, so this has a positive slope. This has an even more positive slope, an even more positive slope. This has an even more positive slope. As x is increasing, the y value is increasing really fast. This line is going up really fast as we move towards the right, so it's a very positive slope. This is less positive, less positive. This is a 0 slope, and then this is a negative slope. Notice, as x is increasing, the line is going down. Your y value is decreasing. When x is negative 5, your y is 7. Well, when x is 5, your y is 5. So x is increased, but y has gone down, so this is a negative slope. So they say graph a line that has a slope that is negative and greater than the slope of the blue line. So the blue line also has a negative slope. As x is increasing, your blue line is going down. Over here, when x has negative values, your y value is quite high. And here, when x has positive values, your y value has gone all the way down. So this has a negative slope, but we want to have a slope greater than this one. So we still want to have a-- they say graph a line that has a slope that is negative-- so my orange line currently has a negative slope-- and greater than the slope of the blue line. So it has a negative slope, but it is less negative than this blue line right over here. If I wanted to be more negative than the blue line, I'd have to do something like that. But I want to be negative but less negative than the blue line, so that would be like that. If we wanted a 0 slope, once again, something like this. If we wanted a positive slope, something like this. So once again, negative slope, less negative than the blue line. Check our answer.