# 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 (*x*_{1},*y*_{1}), then the equation of the line is

*y*-*y*_{1}=*m*(*x*-*x*_{1})

##### 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 *x*_{1} and *y*_{1}, 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 *x*_{1}, and the matching *y*-value for *y*_{1}, 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 *x*_{1} with the known *x*-value (-1) and replace *y*_{1} with the matching *y*-value (5).

*y*-*y*_{1}=*m*(*x*-*x*_{1})*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 = -3*x*- 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*= -3*x*+ 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).

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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