Formula
y = b
Used to calculate:
The y-coordinate where a nonvertical line written in slope-intercept form crosses the y-axis.
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What Is the Y-Intercept Formula?
The y-intercept identifies the point where a line crosses the y-axis. At the y-intercept, the x-coordinate equals zero. For a line written in slope-intercept form, setting x=0 gives y=b, so the y-intercept is determined by the constant term b.
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Formula and Variables
y = b
| Symbol | Meaning | Unit |
| y | y-coordinate of the y-intercept | Same unit as y |
| b | y-intercept value in slope-intercept form | Same unit as y |
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How to Use the Formula
Write the line in slope-intercept form and identify the constant term b. Because x=0 on the y-axis, the corresponding y-value is b. The complete y-intercept point is (0,b).
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When Is This Formula Used?
The y-intercept formula is used to determine where a nonvertical linear equation or function crosses the y-axis.
Common uses:
– Finding the y-intercept of a linear equation
– Graphing straight lines
– Identifying the initial value of a linear relationship
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Important Notes
– At a y-intercept, x=0.
– Every nonvertical line has exactly one y-intercept. A vertical line x=c has a y-intercept only when c=0; in that case, the line is the y-axis itself rather than having a single y-intercept point.
– The y-intercept has the same unit as the y-variable.
– A common point of confusion is reporting only b when an intercept is requested as a coordinate. The y-intercept point is (0,b).
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Alternate Forms
Alternate form:
(0,b)
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