A linear equation is one that relates the first power of two variables, x and y, and its graph is always a straight line. The standard form of such an equation is
where A, B and C are constants.
Every straight line has slope, usually designated by the letter m. Slope is defined as the change in y divided by the change in x between any two points (x1, y1) and (x2, y2) on the line.
If the line passes through point (a, b) and any other random point (x, y), slope can be expressed as:
This can be simplified to produce the slope-point form of the line:
The y-intercept of the line is the value of y when x = 0. The point (a, b) becomes (0, b). Substituting this into the slope-point form of the equation, you get the slope-intercept form:
You now have all you need to find the slope of a line with a given equation.
General Approach: Convert from Standard to Slope-Intercept Form
If you have an equation in standard form, it takes just a few simple steps to convert it to slope intercept form. Once you have that, you can read slope directly from the equation:
has the form
Example 1: What is the slope of the line
In this example, A = 2 and B = 3, so the slope is
Example 2: What is the slope of the line
You can convert this equation to standard form, but if you're looking for a more direct method to find slope, you can also convert directly to slope intercept form. All you have to do is isolate y on one side of the equal sign.
This equation has the form y = mx + b, and
About the Author
Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.