The Slope Formula -

Formula

m = \frac{y_2-y_1}{x_2-x_1}

Used to calculate:

The slope of a nonvertical line from the coordinates of two distinct points on the line.

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What Is the Slope Formula?

The slope formula calculates the rate of change of a line using two points on that line. It compares the change in the vertical coordinate, or rise, with the change in the horizontal coordinate, or run.

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Formula and Variables

m = \frac{y_2-y_1}{x_2-x_1}

Symbol	Meaning	Unit
$m$	Slope of the line	Units of y per unit of x
$x_1$	x-coordinate of the first point	Depends on the problem
$y_1$	y-coordinate of the first point	Depends on the problem
$x_2$	x-coordinate of the second point	Depends on the problem
$y_2$	y-coordinate of the second point	Depends on the problem

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How to Use the Formula

Identify two distinct points on the line and label their coordinates consistently as ( $x_1$ , $y_1$ ) and ( $X_2$ , $Y_2$ ). Subtract the y-coordinates in the same order as the x-coordinates, then divide the change in y by the change in x. The resulting value is the slope of the line.

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When Is This Formula Used?

The slope formula is used to measure the steepness and direction of a straight line or the constant rate of change between two variables in a linear relationship.

Common uses:

– Finding the slope of a line from two points
– Measuring a constant rate of change
– Analyzing linear relationships in algebra, geometry, science, and other quantitative fields

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Important Notes

– A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope represents a horizontal line.
– The x-coordinates must be different: $x_2 \ne x_1$ . A vertical line has an undefined slope because the denominator would be zero.
– If x and y represent different types of quantities, slope has units of y per unit of x. If they use the same unit, the slope is dimensionless.
– A common point of confusion is reversing the subtraction order for only one pair of coordinates. The order must be consistent in both the numerator and denominator.

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Alternate Forms

Alternate form:

m = \frac{\Delta y}{\Delta x}

Alternate form:

\Delta y = m\Delta x

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