How to Find the Slope from a Linear Equation

Finding the Slope from a Linear Equation

The slope of a line is its steepness.

It is how far up a line goes compared to how far across it goes. The line below has a slope of 2 because it goes up 2 units for every 1 unit it goes across.

The slope of the line is 2 because it goes up 2 units for every 1 it goes across

A line can be represented by a linear equation. We can find the slope from a linear equation.

Real Examples of Finding the Slope from a Linear Equation

Finding the slope of a line from a linear equation is easy.

Here are some linear equations, which represent lines. We show how to find the slope from the linear equation.

  • The slope of y = 2x + 1 is 2.

    slope of y equals 2 x plus 1 is 2

    Look at the number in front of the x (called the coefficient of x). This is the slope.

    A slope of 2 means that the line will go up by 2 when it goes across by 1.

  • The slope of y = −3x + 3 is −3.

    slope of y equals minus 3 x plus 3 is minus 3

    The number in front of the x is negative. This means the line slopes downwards.

    A slope of −3 means that the line will go down by 3 when it goes across by 1.

  • y = 2 is a horizontal line. It has a slope of 0.

    slope of y equals 2 is 0

    y = 2 does not have an x in it. We can imagine there is an invisible 0 in front of the x which gets rid of it.

    A slope of 0 means that the line will neither go up nor down when it goes across by 1.

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A linear equation (in slope-intercept form) is given in the form below:

y = mx + c

The m gives the slope of the line.

The slider below explains why the m in a linear equation gives the slope:

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See Also

What is the slope of a line? What is a linear equation?