About this video
The video graphs a line with slope -2 through the point (4, -3). Starting at (4, -3), a slope of -2 means when x increases by 1, y decreases by 2, giving a second point (5, -5). It also shows the alternative of decreasing x by 1 and increasing y by 2, which gives the same line.
You'll be able to
- plot a given point on the coordinate plane.
- use a slope to find a second point on a line.
- explain why moving right 1 and down 2, or left 1 and up 2, gives the same line for slope -2.
Key words
- slope
- How steep a line is: the change in y divided by the change in x.
- change in y
- How much the y-value goes up or down between two points.
- change in x
- How much the x-value goes left or right between two points.
Transcript
- [Instructor] We are told graph a line with the slope of negative two, that contains the point four comma negative three. And we have our little Khan Academy graphing widget right over here, where we just have to find two points on that line, and then that will graph the line for us.
So pause this video and even if you don't have access to the widget right now, although it's all available on Khan Academy, at least think about how you would approach this. And if you have paper and pencil handy, I encourage you to try to graph this line on your own, before I work through it with this little widget.
All right, now let's do it together. So we do know that it contains point four comma negative three. So that's I guess you could say the easy part, we just have to find the point x is four y is negative three. So it's from the origin four to the right, three down.
But then we have to figure out where could another point be? Because if we can figure out another point, then we would have graphed the line. And the clue here is that they say a slope of negative two. So one way to think about it is, we can start at the point that we know is on the line, and a slope of negative two tells us that as x increases by one, y goes down by two.
The change in why would be negative two. And so this could be another point on that line. So I could graph it like this is x goes up by one, as x goes from four to five, y will go, or y will change by negative two. So why we'll go from negative three to negative five.
So this will be done, we have just graphed that line. Now another way that you could do it, because sometimes you might not have space on the paper, or on the widget to be able to go to the right for x to increase, is to go the other way. If you have a slope of negative two, another way to think about it is, if x goes down by one, if x goes down by one, then y goes up by two.
'Cause remember, slope is change of y over change in x. So you could either say you have a positive change in y of two when x has a negative one change, or you could think of it when x is a positive one change, y has a negative two change. But either way notice, you got the same line.
Notice this line is the same thing, as if we did the first way is we had x going up by one and y going down by two, it's the exact same line.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.