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# Slope & direction of a line

A line that's flat has a slope of 0. If a line goes up as you move to the right, it has a positive slope. The steeper it is, the bigger the slope. If a line goes down as you move to the right, it has a negative slope. The steeper it is, the more negative the slope. Created by Sal Khan.

## Want to join the conversation?

• how do you know if its a positive or negative slope?
• A line has a positive slope if it is slanting upward, toward the right. A line has a negative slope if it is slanting upward, toward the left.
• 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!
• 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.
• In the UK we call slope the Gradient.
• Good point - we call it the Gradient in Australia too. Nearly forgot!
• I'm confused with the undefined slope
• 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.
• What is an undefined slope?
• My math teacher taught it to me as a story, if you go down the ski hill that goes straight up and down, when your body is found, you'll be undefinable.
• This community is so cool. hi to friends 5 years from now! wish you luck <3
• So if the line is horizontal, the slope is zero, right? So what would be the slope of a line that is vertical?
• 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!
• what happens if Sal flipped the line upside-down?
will X become Y & Y become X?
• Interesting question! The transformation that reverses x and y is not an upside down flip, but instead is a reflection about the diagonal line y = x.

Have a blessed, wonderful day!
• Can anyone tell me how is one slope greater than another?
• Slope is understood to be the rate of change in the line (or how steep it is). The steeper the slope, the larger the slope is because it is changing or going up at a faster rate.