The X-Intercept Formula -

Formula

x = -\frac{b}{m}

Used to calculate:

The x-coordinate where a nonvertical linear equation in slope-intercept form crosses the x-axis.

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What Is the X-Intercept Formula?

The x-intercept formula finds the point where a line crosses the x-axis. At an x-intercept, the y-coordinate equals zero. For a line written in slope-intercept form, setting y=0 and solving for x gives the x-intercept.

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Formula and Variables

x = -\frac{b}{m}

Symbol	Meaning	Unit
$x$	x-coordinate of the x-intercept	Same unit as x
$m$	Slope of the line	Units of y per unit of x
$b$	y-intercept	Same unit as y

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How to Use the Formula

Write the line in slope-intercept form, identify the slope m and y-intercept b, and substitute them into the x-intercept formula. The resulting x-value gives the x-coordinate where the line crosses the x-axis. The complete intercept point is (x,0).

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When Is This Formula Used?

The x-intercept formula is used to determine where a nonhorizontal linear function or equation crosses the x-axis.

Common uses:

– Finding the x-intercept of a linear equation
– Graphing straight lines
– Finding the zero or root of a linear function

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Important Notes

– At an x-intercept, y=0.
– The formula $x=-b/m$ requires $m \ne 0$ . If $m=0$ , the line is horizontal: it has no x-intercept when $b \ne 0$ , while $y=0$ itself coincides with the entire x-axis.
– The x-intercept has the same unit as the x-variable.
– A common point of confusion is reporting only x when an intercept is requested as a coordinate. The intercept point is $\left(-\frac{b}{m},0\right)$ .

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Alternate Forms

Alternate form:

\left(-\frac{b}{m},0\right)

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