Standard Form to Slope Intercept Form Calculator

Created by Anna Szczepanek, PhD
Reviewed by Rijk de Wet
Last updated: May 30, 2023


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!

What are slope-intercept and standard forms?

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

Ax + By + C = 0

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:

y = mx + b

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).

πŸ™‹ 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.

How do I convert standard form to slope intercept form?

When you want to rewrite the standard form Ax + By + C = 0 to the slope-intercept form:

  1. Make sure that B is not equal to zero β€” if it is, the slope-intercept form does not exist.
  2. Rewrite your equation as By = -Ax - C.
  3. Divide both sides by B. We get y = -(A/B)x - C/B.
  4. We've found the slope-intercept form! The slope equals -A/B, and the intercept equals -C/A.

As you can see, switching between these two forms of linear equations is not hard β€” but nevertheless, it requires some calculations. It's much quicker to use Omni's standard form to slope intercept form calculator!

How to use this standard form to slope intercept form calculator?

Our tool can do all the work for you. You only need to:

  1. Choose the direction of conversion.
  2. Input data β€” the coefficients of your linear equation.
  3. And... that's it! The solution to your conversion problem appears at the bottom of our standard form to slope intercept form calculator!
  4. You can adjust the precision of computations by hitting the Advanced mode button and changing the value of the variable Precision.

πŸ”Ž 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 β€” and in the latter, their product must equal -1. Discover more with the following tools:

FAQ

How do I convert slope intercept form to standard form?

To rewrite the slope-intercept form y = mx + b to the standard form, you need to:

  1. Move all the terms to one side of the equality sign. Remember about changing the signs!
  2. Rearrange the equation so that the term with x is first, then the term with y, and then the intercept last.
  3. We now have mx - y + b = 0 and... this is already the standard form! Indeed, the coefficients are: A = m, B = -1, and C = b.

Does the slope-intercept form always exist?

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.

What is the slope-intercept form of x+y=0?

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.

What is the standard form of y=2x-1?

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.

Anna Szczepanek, PhD
Setup
Standard form to slope intercept form
Ax + By + C = 0  β†’  y = mx + b
Your coefficients
A
B
C
Results
Enter the coefficients.
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