Finding the Slope from a Linear Equation in Slope-Point Form
(KS3, Year 9)

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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

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. 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. 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.

Lesson Slides

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:

Beware

Be Careful

In this lesson, we have said that the slope is given by the number in front of the brackets with the x in it. This is true as long as the x in the brackets is positive and doesn't have another number in front of it. For example, consider the linear equations shown below:

The x has a − sign in front of it:
y − 1 = 2(−x − 1)
The slope would be −2.
The x has a number front of it:
y − 1 = 2(3x − 1)
The slope would be 6 (2 × 3).