y Intercept Calculator
This yintercept calculator is the perfect tool to calculate the x and yintercept of any given line. Additionally, you can use it to find the line equation from its slope and the x or yintercept.
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 yintercept of any line?
 How do you find the xintercept 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 2dimensional space as:
where:
 $a$ is the coefficient of the $x$ term;
 $b$ is the coefficient of the $y$ term;
 $c$ is the constant term; and
 $x$ and $y$ 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 yintercept of this line as the point at which it crosses (or intersects) the yaxis. Specifically, it refers to the ycoordinate of this point, although it is also common to call the point itself the yintercept.
Similarly, the line's xintercept would be the point (or the xcoordinate) where it intersects the xaxis.
The slope (or gradient) of a line is the amount of change in $y$ for a change in $x$. You can learn more about the slope of a line using our slope calculator.
We can express the slope, yintercept and xintercept of any line $ax + by + c = 0$ using these equations:
where:
 $y_c$ is the yintercept of the line;
 $x_c$ is the xintercept of the line; and
 $m$ 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.
Slopeintercept form
We can also express a line equation in terms of its slope and yintercept:
where:
 $m$ is the line's slope; and
 $c$ is the line's yintercept, i.e. $c = y_c$.
We could rewrite it to include the yintercept from the start:
You'll find this form very useful when formulating most line equations if you can calculate the slope and yintercept beforehand.
How do you find the yintercept of a line?
To find the yintercept 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 yintercept y_{c}, as y_{c} = −c/b.
 Verify your results using our yintercept calculator.
Or, if the line equation is in the slopeintercept form y = mx + c, you can directly extract the term c as the line's yintercept y_{c}.
For example, consider a line given by the equation $2x + 3y 2 = 0$. The yintercept lies on the intersection of the yaxis (the line defined by $x=0$) and our line $2x + 3y 2 = 0$. So, we insert $x=0$ in $2x + 3y 2 = 0$ to obtain:
How do you find the xintercept of a line?
To find the xintercept 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 yintercept x_{c}, as x_{c} = −c/a.
 Verify your results using our yintercept calculator.
These steps are applicable even if the line equation is in slopeintercept form: y = mx + c, giving you x_{c} = −c/m.
Again, consider the line $2x + 3y 2 = 0$. Its xintercept lies on the intersection point of the xaxis ($y=0$) and $2x + 3y 2 = 0$. So, we insert $y=0$ in $2x + 3y 2 = 0$ to obtain:
How do you find the line equation from its intercepts?
To find the line equation from its xintercept (x_{c}, 0) and yintercept (0, y_{c}), follow these steps:
 Determine the slope m of the line using m = (0 − y_{c})/(x_{c} − 0) to get m = −y_{c}/x_{c}.
 Formulate the line equation in the slopeintercept 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 $2x + 3y 2 = 0$ with $(1,0)$ xintercept and $(0,\frac{2}{3})$ yintercept. Can we find the line equation with just these intercepts? Let's find out.
 We can determine the slope $m$ of this line using these two intercept points $(0,\frac{2}{3})$ and $(1,0)$:
 Formulate the line equation in the slopeintercept form $y = mx + c$:
 Simplify this equation and rearrange it to get $2x + 3y  2 = 0$.
How to calculate x and yintercepts using this yintercept calculator
You can use this yintercept calculator in three modes:

To calculate the x and yintercepts 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
, andc
, and the calculator will provide you with all the answers!
 Choose the mode "Line equation is

To calculate the slope, yintercept, and xintercept of a line from its slopeintercept form:
 Choose the mode "Line equation is
y = mx + c
".  Enter the values for
m
andc
.  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
xintercept
andyintercept
.  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, yintercept, and xintercept of a line.
FAQ
What is the yintercept of the line 2x + 3y = 9?
−3
is the yintercept of the line 2x + 3y = −9
. To find this yourself, follow these steps:
 Substitute
x = 0
into the line's equation to get2×0 + 3y = −9
, or3y = −9
.  Divide both sides by
3
to gety = −3
.  Verify your results using our yintercept calculator.
Do all straight lines have a yintercept?
No. Some lines run parallel to the yaxis, and thus don't have a yintercept. However, every line in two dimensions has at least one intercept, be it x or yintercept.