How to Find the Slope from a Linear Equation in General Form
Finding the Slope from a Linear Equation in General 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.
A line can be represented by a linear equation. We can find the slope from a linear equation.
How to Find the Slope from a Linear Equation in General Form
A linear equation (in general form) is given in the form below:
The a, b and c do not immediately tell you anything about the line (such as its slope or yintercept).
But it can be converted to a form which does tell you about the line. For example, the slopeintercept form gives the slope and yintercept.
It is the m in the slopeintercept form that tells you the slope.
Once we know the slopeintercept form, we can read off the number in front of the x (the m) to find the slope.
We can use algebra to convert the general form into the slopeintercept form:
Comparing this with y = mx + c, we see that the slope is −^{a}⁄_{b}.
Read more about converting a linear equation in general form to slopeintercept form
A Real Example of Finding the Slope from a Linear Equation in General Form
Finding the slope of a line from a linear equation in general form is easy.
Question
Find the slope of the line given by the linear equation shown below.
StepbyStep:
1
Find the number in front of the x. In our example, the number in front of the x is 4.
4x + 2y + 2 = 0
2
Find the number in front of the y. In our example, the number in front of the y is 2.
4x + 2y + 2 = 0
3
Divide the number from Step 1 (4) by the number from Step 2 (2).
4 ÷ 2 = 2
4
Answer:
The slope is −2.
More Examples of Finding the Slope of a Line from Linear Equations
All of the linear equations we have seen in this lesson have been in general form (ax + b + c = 0).
There are other forms of linear equation. You must be able to find the yintercept in all forms of linear equation.

You need to be able to find the slope of a linear equation in slopeintercept form:
Read more about finding the slope from a linear equation in slopeintercept form

You need to be able to find the slope of a linear equation in slopepoint form:
Read more about finding the slope from a linear equation in slopepoint form