Algebra: Point-Slope Form

Point-Slope Form

If you are given the slope of a line and one of the points on the line, then creating the equation of that line is a very simple procedure. All you'll need is the point-slope formula for a line.

Point-slope formula: If a line has slope m and passes through the point (x1,y1), then the equation of the line is

  • y - y1 = m(x - x1)
Critical Point

Remember, no matter which of the techniques described in this section you use to find a linear equation, you always need two things: the slope of the line and a point on the line.

Critical Point

Variables with subscripts, like x1 and y1, will have completely different values than their non- subscripted look-alikes, x and y. By the way, that little subscript does not affect the value of the variable at all, like an exponent would. It's just a little garnish that distinguishes between the variables, making them different.

Are you wondering where that m came from? For some reason, math people have used the variable m to represent the slope of a line for a long time. Believe it or not, no one quite knows why. I could wax historical about this mathematical conundrum, but you'd get bored fast, so let me suffice to say that m is the variable used to represent slope in all of the formulas you'll see in this section.

Basically, all you have to do to create a linear equation is to plug in a slope for m, an x-value from an ordered pair for x1, and the matching y-value for y1, and simplify.

Example 1: Write the equation of the line with slope -3 that passes through the point (-1,5) and solve the equation for y.

Solution: Since the slope equals -3, set m = -3 in the point-slope formula. You should also replace x1 with the known x-value (-1) and replace y1 with the matching y-value (5).

  • y - y1 = m(x - x1)
  • y - (5) = -3(x - (-1))
You've Got Problems

Problem 1: Write the equation of the line with slope 4 that passes through the point (2,-7) and solve the equation for y.

Simplify the right side of the equation.

  • y - 5 = -3(x + 1)
  • y - 5 = -3x - 3

Since the problem asks you to solve for y, you should isolate it on the left side of the equation by adding 5 to both sides.

  • y = -3x + 2

That's all there is to it! This is the only line in the world that has slope -3 and passes through the point (-1,5).

CIG Algebra

Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.

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