X and Y Intercept Calculator
Find the x and y intercepts of a line using the intercept calculator below.
X and Y Intercepts:
xintercept:  1


yintercept:  1

slope (m):  1

Line Graph:
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slope (m): 
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On this page:
 Calculator
 How to Find the YIntercept
 YIntercept of a Line in SlopeIntercept Form
 YIntercept of a Line in Standard Form
 YIntercept of a Line in PointSlope Form
 How to Find the XIntercept
 XIntercept of a Line in SlopeIntercept Form
 XIntercept of a Line in Standard Form
 XIntercept of a Line in PointSlope Form
 How to Find the Slope From the X and Y Intercept
 How to Graph a Line Using the Intercepts
 References
How to Find the YIntercept
The yintercept of a line or curve is the point where the line crosses the yaxis. More specifically, the yintercept is the ycoordinate of the point on the line that has an xcoordinate equal to 0.
Given the equation of a line, you can find the yintercept by setting the value of the x variable in the equation equal to zero (0).
For example, given a linear function f(x) = y, you can find the yintercept by setting x to 0 so that f(0) = b. For a line, you can use the following methods to calculate the point where the line crosses the yaxis.
YIntercept of a Line in SlopeIntercept Form
Slopeintercept form is one of the most frequently used equations to express a straight line.
The slopeintercept form equation is:^{[1]}
y = mx + b
In the slopeintercept formula, the variable b is equal to the yintercept. So the yintercept is equal to b, or the point (0, b).
YIntercept 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 yintercept for a line in standard form, set the value of x to 0 and solve the equation for y.
A(0) + By = C
By = C
By / B = C / B
y = C / B
So, the yintercept 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 yintercept is slightly different:
A(0) + By + C = 0
By + C = 0
By + C – C = C
By / B = –C / B
y = –C / B
YIntercept of a Line in PointSlope Form
Pointslope form is another commonly used linear equation format.
The pointslope form equation is given by:^{[3]}
y – y_{1} = m(x – x_{1})
Like before, set the value of x to 0 to solve for y.
y – y_{1} = m(0 – x_{1})
y – y_{1} = mx_{1}
y – y_{1} + y_{1} = mx_{1} + y_{1}
y = y_{1} – mx_{1}
The yintercept for a line expressed in pointslope form is equal to y_{1} – mx_{1} or the point (0, y_{1} – mx_{1}).
How to Find the XIntercept
The xintercept of a line or curve is the point where the line crosses the xaxis. The xintercept is the xcoordinate of the point on the line that has a ycoordinate equal to 0.
You can find the xintercept of a line by following the same steps as solving the yintercept, except that instead of setting the value of x to zero, you’ll be setting the value of y to 0.
XIntercept of a Line in SlopeIntercept Form
Recall the slopeintercept form equation from above:
y = mx + b
To find the xintercept, set the value of y to 0 and solve for x.
0 = mx + b
0 – b = mx + b b
b = mx
–b / m = mx / m
–b / m = x
For a line in slopeintercept form, the xintercept is equal to b/m, or the point (b/m, 0).
XIntercept of a Line in Standard Form
Recall the standard form equation from above:
Ax + By = C
To find the xintercept, set the value of y to 0 and solve for x.
Ax + B(0) = C
Ax = C
Ax / A = C / A
x = C / A
For a line in standard form, the xintercept is equal to C/A, or the point (C/A, 0).
XIntercept of a Line in PointSlope Form
Recall the pointslope form equation is:
y – y_{1} = m(x – x_{1})
To solve the xintercept, set the value of y to 0 and solve for x.
0 – y_{1} = m(x – x_{1})
y_{1} = m(x – x_{1})
y_{1} / m = m(x – x_{1}) / m
y_{1} / m + x_{1} = x – x_{1} + x_{1}
x_{1} – y_{1} / m = x
y_{1} + mx_{1} = mx – mx_{1} + mx_{1}
y_{1} + mx_{1} = mx
(y_{1} + mx_{1}) / m = mx / m
(mx_{1} – y) / m = x
Thus, the xintercept for a line in pointslope form is (x_{1} – y_{1})/m, or the point (x_{1} – y_{1})/m, 0).
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 = y_{2} – y_{1} / x_{2} – x_{1}
The intercepts can be treated just as any other points on the line. So, if you substitute the points (0, y) and (x, 0) into the slope formula, you can find the slope.
m = 0 – y / x – 0
m = –y / x
Thus, the slope of the line is equal to the negative yintercept divided by the xintercept.
How to Graph a Line Using the Intercepts
Since the xintercept and yintercept 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, the xintercept being on the xaxis and the yintercept being on the yaxis, then connect them with a line, extending the line indefinitely to both sides of the graph.
References
 CK12 Foundation, Linear Equations in SlopeIntercept Form, https://www.ck12.org/book/ck12algebrabasic/section/5.1/
 IXL, Standard form of linear equations, https://www.ixl.com/math/lessons/standardformoflinearequations
 Clapham, C., Nicholson, J., Oxford Concise Dictionary of Mathematics, 475. https://web.archive.org/web/20131029203826/http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf