The Slope-Intercept Form Formula -

Formula

y = mx + b

Used to calculate:

The value of y on a straight line from its slope, y-intercept, and x-coordinate.

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What Is the Slope-Intercept Form Formula?

The slope-intercept form is a way to represent a nonvertical linear equation using the line’s slope and y-intercept. The coefficient of x gives the slope of the line, while the constant term gives the y-coordinate where the line crosses the y-axis.

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Formula and Variables

y = mx + b

Symbol	Meaning	Unit
$y$	Dependent variable or y-coordinate	Depends on the problem
$x$	Independent variable or x-coordinate	Depends on the problem
$m$	Slope or rate of change	Units of y per unit of x
b	y-intercept	Same unit as y

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How to Use the Formula

Identify the slope and y-intercept of the line. Substitute these values for m and b, then use a known x-value to calculate the corresponding y-value. The equation can also be used to identify the slope and y-intercept directly when a linear equation is already written in slope-intercept form.

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When Is This Formula Used?

Slope-intercept form is used to represent, analyze, and graph nonvertical straight lines when their slope and y-intercept are known or can be determined.

Common uses:

– Writing equations of straight lines
– Graphing linear equations
– Modeling constant rates of change with an initial value

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Important Notes

– The coefficient m determines the line’s slope, while b gives its y-intercept at (0,b).
– Vertical lines cannot be represented in slope-intercept form because their slope is undefined.
– The terms y, mx, and b must have compatible units; therefore, m has units of y per unit of x.
– A common point of confusion is interpreting b as an x-intercept. In slope-intercept form, b represents the y-intercept.

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Alternate Forms

Alternate form:

m = \frac{y-b}{x}

for

x \ne 0

Alternate form:

x = \frac{y-b}{m}

for

m \ne 0

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