X and Y Intercept Calculator

Find the x and y intercepts of a line using the intercept calculator below.

Point #1 Coordinates:
Point #2 Coordinates:
Point Coordinates:
Slope-Intercept Form Equation:
y = mx + b
Point-Slope Form Equation:
y - y1 = m(x - x1)
Standard Form Equation:
Ax + By = C

X and Y Intercepts:

x-intercept:
-1
y-intercept:
1
slope (m):
1

Line Graph:

Learn how we calculated this below


On this page:


How to Find the Y-Intercept

The y-intercept of a line or curve is the point where the line crosses the y-axis. More specifically, the y-intercept is the y-coordinate of the point on the line that has an x-coordinate equal to 0.

Graphic showing the y-intercept is the point where the line crosses the y-axis

Given the equation of a line, you can find the y-intercept by setting the value of the x variable in the equation to zero (0).

For example, given the function f(x) = y, you can find the y-intercept by setting x to 0. For a linear line, you can use the following methods to calculate the point where the line crosses the y-axis.

Y-Intercept of a Line in Slope-Intercept Form

Slope-intercept form is one of the most frequently used equations to express a straight line.

The slope-intercept form equation is:[1]

y = mx + b

In the slope-intercept formula, the variable b is equal to the y-intercept. So the y-intercept is equal to b, or the point (0, b).

Y-Intercept of a Line in Standard Form

Standard form (or general form) is the standard format for the equation of a straight line.

The standard form line equation is:[2]

Ax + By = C

To find the y-intercept for a line in standard form, set the value of x to 0 and solve the equation.

A(0) + By = C
By = C
By / B = C / B
y = C / B

So, the y-intercept of the line is equal to C/B or the point (0, C/B).

Some uses of the standard form use an alternate version of the equation:

Ax + By + C = 0

In this variation of the equation, the y-intercept is different:

A(0) + By + C = 0
By + C = 0
By + C – C = -C
By / B = –C / B
y = –C / B

Y-Intercept of a Line in Point-Slope Form

Point-slope form is another commonly used straight-line equation.

The point-slope form equation is:[3]

y – y1 = m(x – x1)

Like before, set the value of x to 0 to solve the y-intercept.

y – y1 = m(0 – x1)
y – y1 = -mx1
y – y1 + y1 = -mx1 + y1
y = y1 – mx1

The y-intercept for a line expressed in point-slope form is equal to y1 – mx1 or the point (0, y1 – mx1).

How to Find the X-Intercept

The x-intercept of a line or curve is the point where the line crosses the x-axis. The x-intercept is the x-coordinate of the point on the line that has a y-coordinate equal to 0.

Graphic showing the x-intercept is the point where the line crosses the x-axis

You can find the x-intercept of a line by following the same steps as solving the y-intercept, except that instead of setting the value of x to zero, you’ll be setting the value of y to 0.

X-Intercept of a Line in Slope-Intercept Form

Recall the slope-intercept form equation from above:

y = mx + b

To find the x-intercept, set the value of y to 0 and solve.

0 = mx + b
0 – b = mx + b -b
-b = mx
b / m = mx / m
b / m = x

For a line in slope-intercept form, the x-intercept is equal to -b/m, or the point (-b/m, 0).

X-Intercept of a Line in Standard Form

Recall the standard form equation from above:

Ax + By = C

To find the x-intercept, set the value of y to 0 and solve.

Ax + B(0) = C
Ax = C
Ax / A = C / A
x = C / A

For a line in standard form, the x-intercept is equal to C/A, or the point (C/A, 0).

X-Intercept of a Line in Point-Slope Form

Recall the point-slope form equation is:

y – y1 = m(x – x1)

To solve the x-intercept, set the value of y to 0.

0 – y1 = m(x – x1)
-y1 = m(x – x1)
-y1 = mx – mx1
-y1 + mx1 = mx – mx1 + mx1
-y1 + mx1 = mx
(-y1 + mx1) / m = mx / m
(mx1 – y) / m = x

Thus, the x-intercept for a line in point-slope form is (mx1 – y)/m.

How to Find the Slope From the X and Y Intercept

Once you have the x and y intercepts for the line, you can find the slope of the line.

You’ll need the slope formula to find the slope:

m = y2 – y1 / x2 – x1

The intercepts can be treated just as any other point on the line. So, if you substitute the points (0, y) and (x, 0) in the formula, you can find the points.

m = 0 – y / x – 0
m = –y / x

Thus, the slope of the line is equal to the negative y-intercept divided by the x-intercept.

How to Graph a Line Using the Intercepts

Since the x-intercept and y-intercept are points on the line like any other, you can graph the line using them as well.

Plot the intercept points on the axes of the graph, then connect them with a line.

References

  1. CK-12 Foundation, Linear Equations in Slope-Intercept Form, https://www.ck12.org/book/ck-12-algebra-basic/section/5.1/
  2. IXL, Standard form of linear equations, https://www.ixl.com/math/lessons/standard-form-of-linear-equations
  3. Clapham, C., Nicholson, J., Oxford Concise Dictionary of Mathematics, 475. https://web.archive.org/web/20131029203826/http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf