Example of the Slope Formula

[Single Speaker]

[Opening view begins with the title on the screen: Example of the Slope Formula Between Two Points.]

Instructor: This video shows another example of applying the slope formula between two points.

[Title disappears and a graph appears with a line extending down from the point (-4, 2) to the point (5, -1). In the corner is the equation .]

Here’s another line segment with two points. Again, let’s try to figure out the slope using these two points. The first thing I want to do is designate which point is point 1 and which point is point 2. It doesn’t matter which point I choose as point 1 or point 2 as long as I don’t confuse them when I’m putting them into my equation. So the two points on my line are 5 and -1 and -4 and 2. So I’m going to pick 5, -1 as point 1. And I’m going to select -4 , 2 as point 2. [Labels (5, -1) as pt 1, and (-4, 2) as pt 2.] Now I can start plugging these numbers into my slope equation to find the slope of this line. And if we do this correctly, we should get a negative number because our slope is a negative slope.

So let’s plug them in, so m is equal to y2; y2 if we come over to point 2 is the number 2. So 2 minus y1, come over to point number 1 and look at the y value, that’s negative 1. Remember, put in the negative, just because we already have the subtraction sign doesn’t mean that we don’t have this other negative. [Has written the equation m=2-(-1).] Cause the y value is actually gonna be negative 1. Now let’s do the denominator.

X two. So point number 2, X two is gonna be -4, minus an X 1 in point number one is 5. [the equation she now has written on the board is .] Now all we have to do is the calculation. 2 minus a -1 is the same as 2 plus 1 which equals 3. -4 minus 5 is the same as -4 plus a -5 which is -9. [To the right of the equation she now has written the solution .] So we do have a negative number as our slope, so that’s right [she refers to the slope of the line in the graph]. And now we have a fraction that we can actually simplify. 3 goes into both 3 and 9 so we can simplify this by dividing both numbers by 3. 3 divided by 3 is 1, and 9 divided by 3 is 3, and don’t forget the negative sign. [Has written the simplified solution to the right of the last solution: ]. Doesn’t matter if I put it on the numerator, denominator or just out front. It all means the same, as long as there’s one negative sign, it makes the fraction negative.

So our slope here, m equals -1 third (-1/3). [Writes m=]. In other words, if we start at one point and let’s say we go down one unit and over three units, one, two three [draws a line from pt 2 on the graph going straight down 1 unit then from there over 3 units until it touches the line again at the point (-1, 1)] we will hit another point on our line. And that’s how to find the slope given any two points on a line.

[End of Video]