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# Point-slope Form for the Equation of a Line

We can find the equation of a line if we know the slope of the line, m, and a point on the line, (x1, y1). Hereâ€™s how we can derive a formula for this.

 Start with the formula for the slope of a line that passes through the points, (x1, y1), and (x2, y2). m Replace (x2, y2) with (x, y). m Multiply both sides by x - x1. m(x - x1) Simplify the right side. m(x - x1) = y - y1 By tradition, the y terms are written on the left. y - y1 = m(x - x1)

The result is called the point-slope form for the equation of a line.

Note:

(x1, y1) represents a point on the line that we know.

(x, y) represents an unknown point on the line.

Definition

Point-slope Form for the Equation of a Line

The point-slope form for the equation of a line that passes through the point (x1, y1) and has slope m is.

y - y1 = m(x - x1)

Note that m, x1, and y1 are constants, and x and y are variables.

The following linear equations are written in point-slope form:

 Here, (x1, y1) = (-4, 7) and y - 2 = -3(x - 1) Here, (x1, y1) = (1, -2) and m = -3.