How do I 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.

How do you write the y-intercept answer?

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.

What is the answer to slope y-intercept?

The equation for slope-intercept form is: y=mx+b In this form, m is the slope of the line and the b is the y-intercept.

How to find y-intercept when given 2 points?

Use the slope and one of the points to solve for the y-intercept (b). One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

What is an example of the y-intercept?

Here are some examples of y intercepts. The y-intercept of y = 5x 2 + 2 is, (0, 2) because when we substitute x = 0, we get y = 5(0) 2 + 2 = 2. The y-intercept of y = -5e x is (0, -5) because when we substitute x = 0, we get y = -5e 0 = -5.

What is the y-intercept of y?

The y-intercept of a line is the value of y where the line crosses the y-axis . In other words, it is the value of y when the value of x is equal to 0. Sometimes this has true meaning for the model that the line provides, but other times it is meaningless. We will encounter examples of both types in this section.

How do I solve slope intercept?

Slope-intercept form is y = mx + b , where m is the slope, and b is the y-intercept. If you have both of these, just plug them in. If you don't have the intercept, but do have a point, substitute the x, y, and m into the equation and solve for b.

When y =- 6 What is the slope?

The slope is zero. This is the equation of a horizontal line.

How to find slope and y-intercept from a graph?

All that the slope-intercept form (the equation to describe linear equations) is, is an equation ( y=mx+b ) where m (the number that multiples x) is the slope and b (the number that is not multiplying a variable on the right-hand side of the equation) is the y-intercept.

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:

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.