# Standard Form to Slope Intercept Form Calculator

Result:

Do you want to calculate the slope intercept form from the standard form? Our **Standard Form to
Slope Intercept Form calculator** is the right tool for quickly converting the standard form
to slope intercept form.

Have you ever looked at an equation like `3x + 2y = 12`

and thought "What does this equation
mean?" or "How can I graph this?" Converting equations from standard form to slope-intercept form can
make them much easier to understand and work with.

## What are slope-intercept and standard forms?

The **slope-intercept form** is a way to write a linear equation (a line) in the format:
`y = mx + b`

. In this form:

- m represents the slope or steepness of the line
- x and y are the variable coordinates on the graph
- b is the y-intercept, which is where the line crosses the y-axis

For example, the equation `y = 2x + 3`

is in slope-intercept form. The slope is 2 and the
y-intercept is 3.

**Standard form** is a different way to write linear equations, in the format:
`Ax + By = C`

. In this format:

- A and B are the coefficients (numeric values) of the x and y variables
- C is a constant value

The equation `3x + 2y = 12`

is an example in standard form.

While both forms represent the same line, the slope-intercept form is often easier to visualize and graph. So it can be really useful to convert from standard to slope-intercept form.

## How do I convert standard form to slope-intercept form?

Follow these steps to convert any linear equation from standard form (`Ax + By = C`

) to
slope-intercept form (`y = mx + b`

):

Step 1: Rearrange the equation to get y by itself on one side.

For example: `3x + 2y = 12`

becomes `2y = -3x + 12`

Step 2: Identify the coefficients of x and y.

In this example, the x coefficient is -3 and the y coefficient is 2.

Step 3: Determine the slope by dividing the x coefficient by the y
coefficient.

Slope = -3/2 = -1.5

Step 4: Determine the y-intercept by substituting x=0 into the
original equation and solving for y.

`2y = -3(0) + 12`

`2y = 12`

`y = 6`

So the y-intercept is 6.

Step 5: Write the equation in slope-intercept form:
`y = mx + b`

Plugging in m = -1.5 and b = 6, we get: `y = -1.5x + 6`

Let's go through one more example:

Convert the equation `5x - 3y = 15`

to slope-intercept form.

Step 1: `-3y = -5x + 15`

Step 2: The x coefficient is -5, the y coefficient is -3

Step 3: Slope = -5/-3 = 5/3

Step 4: Substitute x=0: `-3y = 15`

-->
`y = -5`

So the y-intercept is -5

Step 5: Put it all together: `y = (5/3)x - 5`

## How to Use Our Standard form to Slope Intercept form Calculator

Our tool can convert the equations for you. Here's how to use it:

- Input the coefficients for the x variable, y variable, and constant term from the original standard form equation.
- Click the calculate button.
- It will then calculate the slope using the x and y coefficients.
- Finally, it will determine the y-intercept by substituting x=0.
- The output will be the equation written in slope-intercept form.

For example, inputting the coefficients 3, 2, and 12 for the equation `3x + 2y = 12`

:

The calculator rearranges to: `2y = -3x + 12`

It calculates the slope as -3/2 = -1.5

Substituting x=0 gives y-intercept = 6

The final equation is `y = -1.5x + 6`

Pretty cool, right? Having the equation in slope-intercept form makes graphing and understanding the line much simpler.

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## FAQ

**What if there is no x or y term in the original equation?**

If there is no x term, the slope is 0. If no y term, the slope is undefined. The calculator will alert
you.

**Can I convert from slope-intercept to standard form?**

Yes! The basic steps are:

1) Multiply both sides by the slope

2) Isolate the x term on one side

3) Move the constant to the other side

**Why is slope-intercept form useful?**

It clearly shows the slope and y-intercept, which are the most important traits for graphing and
understanding a line. Standard form is more difficult to interpret.

**What if the equation has fractions or decimals?**

No problem! The same steps work for any coefficients, including fractional or decimal values. The
calculator can handle these as well.

**How do I graph an equation in slope-intercept form?**

- Plot the y-intercept point by substituting x=0
- Use the slope to determine the rise/run
- Plot another point and connect to the y-intercept

Hopefully this page has helped you understand how to convert linear equations from standard form to the more user-friendly slope-intercept form. Being able to visualize and graph lines is a crucial skill in algebra and beyond. With enough practice converting between forms, graphing will become a breeze!