# Standard Form to Slope Intercept Form Calculator

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).

π 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:

- Make sure that
β if it is, the slope-intercept form`B`

is not equal to zero**does not exist**. **Rewrite**your equation as`By = -Ax - C`

.**Divide both sides by**. We get`B`

`y = -(A/B)x - C/B`

.- 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:

- Choose the
**direction of conversion**. - Input data β the
**coefficients**of your linear equation. - And... that's it! The
**solution to your conversion problem**appears at the bottom of our standard form to slope intercept form calculator! - You can
**adjust the precision of computations**by hitting the`Advanced mode`

button and changing the value of the variable*Precision*.

π 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:

**Move all the terms to one side of the equality sign**. Remember about changing the signs!**Rearrange the equation**so that the term with`x`

is first, then the term with`y`

, and then the intercept last.- 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.

`Ax + By + C = 0`

β `y = mx + b`

*Enter the coefficients.*