How do you calculate the y-intercept?

Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y . On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

How to find y-intercept with 2 coordinates?

Given two points on a line, we can write an equation for that line by finding the slope between those points, then solving for the y-intercept in the slope-intercept equation y=mx+b . In this example, we write an equation of the line that passes through the points (-1,6) and (5,-4).

What is the y-intercept of a table calculator?

Y intercept calculator helps to compute the value of the y-intercept when we are given a linear equation in two variables. The point where a graph crosses the y-axis is known as the y-intercept. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

What is y-intercept example?

Here is an example of a y-intercept. Consider the line y = x+ 3 . This graph meets the y-axis at the point (0,3). Thus (0,3) is the y-intercept of the line y = x+ 3.

How to find the slope and y-intercept?

The equation of the line is written in the slope-intercept form, which is: y = mx + b , where m represents the slope and b represents the y-intercept. In our equation, y = 6x + 2, we see that the slope of the line is 6.

What would a y-intercept of 2 look like?

The y -intercept for the y=2 graph is simply the point (0,2) .

What if there are two y-intercepts?

The Y-intercept is the point or points where the line in a graph crosses the y-axis. For a straight line, this will only occur once (unless x is a non-zero constant number, in which case there will be no y-intercept), but if a graph does not have a straight line, there can be several y-intercepts in the same graph .

How is the y-intercept calculated?

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable. To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x.

How to find the y-intercept on a calculator?

Press the "Trace" button. Press the "0" button. This will move the cursor to the Y intercept where X = 0. Look at the bottom of your screen; the Y-intercept will be displayed there.

y Intercept Calculator (2024)

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

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_c, as 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_c, as 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_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 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!
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.
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.

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.