How to Find the Slope from a Linear Equation in Slope-Point Form

Finding the Slope from a Linear Equation in Slope-Point Form

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 in Slope-Point Form

Finding the slope of a line from a linear equation in slope-point form 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 − 4 = 2(x − 1) is 2.

    slope of y minus 4 equals 2 (x minus 1) is 2

    Look at the number in front of the brackets with the x in it. This is the slope.

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

  • slope of y − 1 = −3(x − 3) is −3.

    slope of y minus 1 equals minus 3 (x minus 3) is minus 3

    The number in front of the brackets 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.

Slider

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

y − y1 = m(x − x1)

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? What is a linear equation in slope-point form?