The LessonThe 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 FormA 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 y-intercept). But it can be converted to a form which does tell you about the line. For example, the slope-intercept form gives the slope and y-intercept.
It is the m in the slope-intercept form that tells you the slope. Once we know the slope-intercept 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 slope-intercept 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 slope-intercept form
A Real Example of Finding the Slope from a Linear Equation in General FormFinding the slope of a line from a linear equation in general form is easy.
QuestionFind the slope of the line given by the linear equation shown below.
Find the number in front of the x. In our example, the number in front of the x is 4.
4x + 2y + 2 = 0
Find the number in front of the y. In our example, the number in front of the y is 2.
4x + 2y + 2 = 0
Divide the number from Step 1 (4) by the number from Step 2 (2).
4 ÷ 2 = 2
Answer:The slope is −2.
Lesson SlidesThe slider below gives a real example of how to find the slope from a linear equation. Open the slider in a new tab
More Examples of Finding the Slope of a Line from Linear EquationsAll 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 y-intercept in all forms of linear equation.
You need to be able to find the slope of a linear equation in slope-intercept form:
Read more about finding the slope from a linear equation in slope-intercept form
You need to be able to find the slope of a linear equation in slope-point form:
Read more about finding the slope from a linear equation in slope-point form
Postive And Negative SlopesA positive slope means the line slopes up and to the right:
A negative slope means the line slopes down and to the right:
Zero Slope And Undefined SlopeA line that goes straight across has zero slope:
A line that goes straight across has an undefined slope: