Main content

## 8th grade

### Course: 8th grade > Unit 3

Lesson 4: Slope- Intro to slope
- Intro to slope
- Slope formula
- Slope & direction of a line
- Positive & negative slope
- Worked example: slope from graph
- Slope from graph
- Slope of a line: negative slope
- Worked example: slope from two points
- Slope from two points
- Slope from equation
- Converting to slope-intercept form
- Slope from equation
- Slope of a horizontal line
- Slope review

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Slope & direction of a line

CCSS.Math:

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

## Want to join the conversation?

- how do you know if its a positive or negative slope?(42 votes)
- 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.(11 votes)

- At2:05, 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 at2:15. However, the video makes the blue line's slope steeper than the orange line's. Why and how?

Thanks!(34 votes)- 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.(5 votes)

- I'm confused with the undefined slope(5 votes)
- 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.(23 votes)

- In the UK we call slope the Gradient.(12 votes)
- Good point - we call it the Gradient in Australia too. Nearly forgot!(9 votes)

- What is an undefined slope?(6 votes)
- 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.(8 votes)

- 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)
- what happens if Sal flipped the line upside-down?

will**X**become**Y**&**Y**become**X**?(3 votes)- 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!(3 votes)

- Can anyone tell me how is one slope greater than another?(2 votes)
- 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.(3 votes)

- 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) - If you had a line that was vertical, would it have a positive slope?(2 votes)
- 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.