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## Slope

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# Graphing a line given point and slope

CCSS.Math:

## Video 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.