Hi, my name is Bassem Saad. I'm an associate math instructor and Ph.D. candidate, and I'm here today for About.com to answer the question: What is rise over run?

Rise Over Run

So recall that we can draw a line onto the x and y axes inside a plane, and from the coordinates on this line, we can come up with an equation for the line. An important number in the equation is this 'm.' It's so important, it has its own name - it's called the slope; and it's calculated by dividing the rise by the run.

Slope and Rise Over Run

So the slope equals the difference in the y value, divided by the difference in the x value. The difference in the y value is called the rise; and the difference in the x value is called the run. You take any two points on the line, and the rise is going to be the height of the first point, subtracted into the height of the second point: that is, y-one, minus y-zero. And the run will be – you take the corresponding x values of the first point and the second point: that is, your initial x value on the x-axis, x-zero, and you subtract that into x-one. So that is x-one, subtracted by x-zero.

Example of Rise Over Run

Say we want to know the slope of the line going through the points (one, four) and the other point (three, two). Well, the slope is just rise over run; rise is the difference in the y direction. So the first point is (one, four), the y value being four. The second point is (three, two); that means the second y value is two. So you've got two, minus four – that's negative two. And run is just the difference in the x direction. So the first point is (one, four), so the x value is one. The second x value is three. So that's three, minus one, which is two. So rise over run: that's minus two, divided by two - that just equals negative one. So you'll find any line that starts from the upper-left, and moves all the way down to the bottom-right will have negative slope. So now we know what rise over run is.

Thanks for watching, and to learn more visit us on the web at About.com.

Rise Over Run

So recall that we can draw a line onto the x and y axes inside a plane, and from the coordinates on this line, we can come up with an equation for the line. An important number in the equation is this 'm.' It's so important, it has its own name - it's called the slope; and it's calculated by dividing the rise by the run.

Slope and Rise Over Run

So the slope equals the difference in the y value, divided by the difference in the x value. The difference in the y value is called the rise; and the difference in the x value is called the run. You take any two points on the line, and the rise is going to be the height of the first point, subtracted into the height of the second point: that is, y-one, minus y-zero. And the run will be – you take the corresponding x values of the first point and the second point: that is, your initial x value on the x-axis, x-zero, and you subtract that into x-one. So that is x-one, subtracted by x-zero.

Example of Rise Over Run

Say we want to know the slope of the line going through the points (one, four) and the other point (three, two). Well, the slope is just rise over run; rise is the difference in the y direction. So the first point is (one, four), the y value being four. The second point is (three, two); that means the second y value is two. So you've got two, minus four – that's negative two. And run is just the difference in the x direction. So the first point is (one, four), so the x value is one. The second x value is three. So that's three, minus one, which is two. So rise over run: that's minus two, divided by two - that just equals negative one. So you'll find any line that starts from the upper-left, and moves all the way down to the bottom-right will have negative slope. So now we know what rise over run is.

Thanks for watching, and to learn more visit us on the web at About.com.

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