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Do you want to calculate the slope intercept form from the standard form or the other way around? Our tool can do both and with as much precision as you require! Read on to discover what these two forms of writing down linear equations are all about and how to quickly turn the standard form into the slope intercept form!
The slope-intercept and standard form are two methods of expressing an equation of a line in the two-dimensional plane.
The standard form of a linear equation is
where A , B , and C are constants. Some methods of solving systems of linear equations assume that you have your equations in the standard form.
The slope-intercept form is:
where m and b are coefficients. We call m the slope (because it describes the steepness of the line) and b the intercept (because it is the point on the plane where the line intersects the vertical axis).
🙋 To discover some interesting facts about the applications of this particular form of linear equations, check our dedicated slope intercept form calculator.
Let's learn how to turn standard form into slope-intercept form.
When you want to rewrite the standard form Ax + By + C = 0 to the slope-intercept form:
As you can see, switching between these two forms of linear equations is not hard — but nevertheless, it requires some calculations. It's much quicker to use Omni's standard form to slope intercept form calculator!
Our tool can do all the work for you. You only need to:
🔎 A useful application of the slope-intercept form is to check whether two lines are parallel or perpendicular. In the former case, the slopes must be equal — and in the latter, their product must equal -1 . Discover more with the following tools:
To rewrite the slope-intercept form y = mx + b to the standard form, you need to:
No, for a vertical line, the slope-intercept does not exist because its slope is undefined. The standard form of such a line does not contain the term with the variable y . However, every non-vertical line can be written in the slope-intercept form.
The slope-intercept form is y = -x . That is, the slope is m = -1 , and the intercept is b = 0 . We see this equation describes a decreasing function.
The standard form is -2x + y + 1 = 0 . That is, the coefficients are A = -2 , B = 1 , and C = 1 . The standard form exists for every line written in the slope-intercept form.
