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Slope
(KS3, Year 8)

The slope of a line is its steepness. The larger the slope, the steeper the line.

A line with a high slope is steeper than a line with a low slope

Understanding the Slope of a Line

The slope of a line is how far the line goes up (or down) divided by how far a line goes across (left to right). Look at the line below:

The line goes up by 3 and across by 3 If we draw a triangle under the line and measure how far it goes up and across...
  • The line goes up by 3...
  • ...and across by 3.

Slope = How far up ÷ How far across

Slope = 3 ÷ 3

Slope = 1

The slope of the line is 1.

Real Examples of the Slope of a Line

  • Lines that slope from the bottom-left up to the top-right have a positive slope.

    positive slope of 2 The line above has a slope of 2 because it goes up by 2 squares and across by 1.
  • Lines that slope from the top-left up to the bottom-right have a negative slope.

    negative slope of -2 The line above has a slope of −2 because it goes down by 2 squares and across by 1.
  • Lines that do not slope up nor down have a slope of 0.

    zero slope
  • Lines that do not slope across have an undefined slope.

    undefined slope

Formulas to Find the Slope of a Line

We can find the slope of a line if we know how far it goes up and how far it goes across. In Cartesian coordinates, the y-axis measures how far up a line is and the x-axis measures how far across a line is. This lets us define a formula to find the slope of a line:

slope equals change in y over change in x
finding the slope of a line We can find the slope if we know two points (in Cartesian coordinates) on the line.

slope equals y 2 minus y 1 over x 2 minus x 1
finding the slope between two points

Lesson Slides

The slider below gives more information about the slope of a line.

Rise Over the Run

An easy way to remember the meaning of slope is "rise over run". Rise is how far up (or down) a line goes. Run is how far across a line goes.

rise over run

A Slope of 1

A slope of 1 gives a 45° line. It goes up and across by the same amount.

slope of 1

Fractional Slopes

A slope can be a fraction such as ½ or ¾.

slope of a half A fractional slope is still positive (slopes from bottom-left to top-right) but it is less steep than a slope of 1.
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This page was written by Stephen Clarke.

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