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(male narrator) In this video,
we will begin looking
at how we can find the slope of a line given two points.
Slope, we have said, is represented with the letter m,
which is calculated by the rise over the run.
When we say the rise over the run,
the rise can be thought of as the change in y.
And the run, because it's horizontal,
is the amount of change that occurs in the x-values.
So to get a formula to find the change in the y-values,
we will subtract the two y-values
to find out how much the y's change.
And we will subtract the second x, minus the first x,
to find the amount of change
that's happening in the x-values.
Let's take a look at how we can use this formula--
y2 minus y1, over x2, minus x1--
to find the slope between two points.
Here, we have a set of points-- x,y: 7,2; and x,y: 11,4.
We'll call 7,2 the first point and the 11,4 the second point.
The formula for slope, we said,
was y2, minus y1, over x2, minus x1.
By plugging in our numbers, we can calculate the slope.
y2 is the y-value from the second point--
this times, it's 4;
minus y1, which is the y-value from the first point--
this one is 2;
over x2--the x-value from the second point,
which is 11;
minus x1--or the x-value from the first point,
which is 7.
By subtracting 4 minus 2 is 2, over 11 minus 7 is 4,
and reducing, we find the slope of this line
that connects the two points-- 7,2 and 11,4--is 1/2.
This means for every one unit the graph rises,
it will also run two units.
Let's take a look at another example
where we find the slope between two points
using the slope formula.
Here, we have two new points:
-2,-5 is our first x,y-- our first point;
-17,4 is our second x,y-- our second point.
So when we come to the equation...
whoops...when we have the equation,
m is equal to y2, minus y1, over x2, minus x1,
we simply have to plug in the points we found.
y2 is the y from the second point.
This would be 4;
minus y1--y from the first point--would be -5;
over x2--x from the second point--is -17;
minus x1--x from the first point--is -2.
By subtracting,
or subtracting a negative becoming...adding a positive,
we can find our slope:
4 plus 5 is 9; over -17, plus 2, is -15.
Reducing this fraction by dividing by 3
gives us 3/5-- not forgetting the negative.
The slope between these points is -3/5.
This means for every 3 units the graph goes down,
it will also run a horizontal distance of 5.
Notice because the slope is negative,
we know this line is going downhill from left to right.
Being familiar with the slope formula--
y2 minus y1, over x2, minus x1--
can help us find the slope of any graph.