This **y-intercept calculator** is the perfect tool to calculate the **x-** and **y-intercept** of any given line. Additionally, you can use it to find the **line equation** from its slope and the x- or y-intercept.

Finding intercepts of straight lines is a simple process, but it is pretty common to get the basics mixed up. Let's discuss the following basics in this article so that you're always ready:

- How do you find the
**y-intercept**of any line? - How do you find the
**x-intercept**of any line? - How do you find the
**line equation**from its**intercepts**?

If you're interested in finding the line equation in different forms, we recommend our popular slope intercept form calculator and point slope form calculator.

## Slope, intercepts, and the general line equation

We can express the most **general form** of a **straight line** in **2-dimensional space** as:

$ax + by + c = 0$ax+by+c=0

where:

- $a$a is the
**coefficient**of the $x$x term; - $b$b is the
**coefficient**of the $y$y term; - $c$c is the
**constant**term; and - $x$x and $y$y are the
**variables**representing the two dimensions.

You can plot this line on a graph sheet if you know at least two points that lie on this line. We define the **y-intercept** of this line as the point at which it **crosses** (or **intersects**) the **y-axis**. Specifically, it refers to the *y-coordinate* of this point, although it is also common to call the point itself the y-intercept.

Similarly, the line's **x-intercept** would be the point (or the *x-coordinate*) where it intersects the **x-axis**.

The **slope** (or **gradient**) of a line is the amount of **change** in $y$y for a **change** in $x$x. You can learn more about the slope of a line using our slope calculator.

We can express the slope, y-intercept and x-intercept of any line $ax + by + c = 0$ax+by+c=0 using these equations:

$\begin{align*}y_c &= - c/b\\x_c &= - c/a \\m &= - a/b\end{align*}$ycxcm=−c/b=−c/a=−a/b

where:

- $y_c$yc is the
**y-intercept**of the line; - $x_c$xc is the
**x-intercept**of the line; and - $m$m is the slope of the line.

In the following sections, we'll prove these equations with an example — but first, let's discuss another form of a line equation.

## Slope-intercept form

We can also express a line equation in terms of its **slope** and **y-intercept**:

$y = mx + c$y=mx+c

where:

- $m$m is the line's
**slope**; and - $c$c is the line's
**y-intercept**, i.e. $c = y_c$c=yc.

We could rewrite it to include the y-intercept from the start:

$y = mx + y_c$y=mx+yc

You'll find this form very useful when formulating most line equations if you can calculate the slope and y-intercept beforehand.

## How do you find the y-intercept of a line?

To find the y-intercept of a line given by *ax + by + c = 0*, follow these simple steps:

**Substitute**the value*x = 0*into the line equation to get*by + c = 0*.**Rearrange**this equation to find the**y-intercept***y*, as_{c}*y*._{c}= −c/b- Verify your results using our y-intercept calculator.

Or, if the line equation is in the slope-intercept form *y = mx + c*, you can directly extract the term *c* as the line's y-intercept *y _{c}*.

For example, consider a line given by the equation $2x + 3y -2 = 0$2x+3y−2=0. The **y-intercept** lies on the intersection of the y-axis (the line defined by $x=0$x=0) and our line $2x + 3y -2 = 0$2x+3y−2=0. So, we insert $x=0$x=0 in $2x + 3y -2 = 0$2x+3y−2=0 to obtain:

$\begin{align*}2\cdot 0+ 3y - 2 &= 0\\3y - 2 &=0\\3y &= 2\\\therefore y_c &= \frac{2}{3}\end{align*}$2⋅0+3y−23y−23y∴yc=0=0=2=32

## How do you find the x-intercept of a line?

To find the **x-intercept** of a line given by *ax + by + c = 0*, follow these simple steps:

**Substitute**the value*x = 0*into the line equation to get*ax + c =0*.**Rearrange**this equation to find the**y-intercept***x*, as_{c}*x*._{c}= −c/a- Verify your results using our y-intercept calculator.

These steps are applicable even if the line equation is in slope-intercept form: *y = mx + c*, giving you *x _{c} = −c/m*.

Again, consider the line $2x + 3y -2 = 0$2x+3y−2=0. Its **x-intercept** lies on the intersection point of the x-axis ($y=0$y=0) and $2x + 3y -2 = 0$2x+3y−2=0. So, we insert $y=0$y=0 in $2x + 3y -2 = 0$2x+3y−2=0 to obtain:

$\begin{align*}2x + 3 \cdot 0 - 2 &= 0\\2x - 2 &=0\\2x &= 2\\\therefore x_c &= 1\end{align*}$2x+3⋅0−22x−22x∴xc=0=0=2=1

## How do you find the line equation from its intercepts?

To find the line equation from its **x-intercept** *(x _{c}, 0)* and

**y-intercept**

*(0, y*, follow these steps:

_{c})**Determine**the**slope***m*of the line using*m = (0 − y*to get_{c})/(x_{c}− 0)*m = −y*._{c}/x_{c}**Formulate**the line equation in the slope-intercept form*y = mx + c*, keeping in mind that*c = y*._{c}**Simplify**and**rearrange**as required, or use the equation as it is.

Once again, let's consider the line $2x + 3y -2 = 0$2x+3y−2=0 with $(1,0)$(1,0) **x-intercept** and $(0,\frac{2}{3})$(0,32) **y-intercept**. Can we find the line equation with just these intercepts? Let's find out.

- We can determine the
**slope**$m$m of this line using these two intercept points $(0,\frac{2}{3})$(0,32) and $(1,0)$(1,0):

$\qquad\begin{align*}m &= \frac{0-\frac{2}{3}}{1-0}\\\therefore m &= -\frac{2}{3}\end{align*}$m∴m=1−00−32=−32

- Formulate the line equation in the slope-intercept form $y = mx + c$y=mx+c:

$\qquad y = -\frac{2}{3}x + \frac{2}{3}$y=−32x+32

- Simplify this equation and rearrange it to get $2x + 3y - 2 = 0$2x+3y−2=0.

## How to calculate x- and y-intercepts using this y-intercept calculator

You can use this **y-intercept** calculator in three modes:

To calculate the

**x-**and**y-intercepts**along with the line's**slope**from its general equation:- Choose the mode "Line equation is
`ax + by + c = 0`

". - Enter the values for
`a`

,`b`

, and`c`

, and the calculator will provide you with all the answers!

- Choose the mode "Line equation is
To calculate the

**slope, y-intercept, and x-intercept**of a line from its slope-intercept form:- Choose the mode "Line equation is
`y = mx + c`

". - Enter the values for
`m`

and`c`

. - Sit back and relax as the calculator takes care of the rest.

- Choose the mode "Line equation is
To find an

**equation**with the**intercepts**given, use the mode "Line equation is**to be determined.**"- Enter the values of
`x-intercept`

and`y-intercept`

. - Enjoy the fast and accurate results.

- Enter the values of

Our calculator will also present you with a summary of results and a helpful graph in all these modes!

Pat yourself on your back for learning something new today! We believe you're ready to explain to others how to find the slope, y-intercept, and x-intercept of a line.

## FAQ

### What is the y-intercept of the line 2x + 3y = -9?

`−3`

is the **y-intercept** of the line `2x + 3y = −9`

. To find this yourself, follow these steps:

**Substitute**`x = 0`

into the line's equation to get`2×0 + 3y = −9`

, or`3y = −9`

.**Divide**both sides by`3`

to get`y = −3`

.- Verify your results using our
**y-intercept calculator**.

### Do all straight lines have a y-intercept?

**No**. Some lines run parallel to the **y-axis**, and thus **don't** have a **y-intercept**. However, every line in two dimensions has **at least one** intercept, be it **x-** or **y-intercept**.