About this video
This video explains how the direction of a line shows its slope: a flat line has slope 0, a line going up to the right has a positive slope, and a line going down to the right has a negative slope. It then graphs a line whose slope is negative but greater than (less negative than) the blue line's, which means a line that slopes down less steeply.
You'll be able to
- tell whether a line's slope is positive, negative or zero from its direction.
- explain that a horizontal line has a slope of 0.
- compare two negative slopes and pick the greater (less negative) one.
Key words
- slope
- How steep a line is and which way it goes as x increases.
- positive slope
- As x increases, y increases, so the line goes up to the right.
- negative slope
- As x increases, y decreases, so the line goes down to the right.
- zero slope
- y does not change as x increases, so the line is flat (horizontal).
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.
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