Day 50 – November 5

Algebra: Chapter 7, Lesson 6, page 328

Finding an Equation of a Line

There are 2 ways that we can find an equation of a line. However, we need to have at least 2 points `(x,y)` or 1 point `(x,y)` and the slope, `m` provided. If we have those things, we can find the equation by the 2 methods below, you choose the one you like:

A. Using the slope-intercept equation, `y=mx+b`

1. (Don’t forget, for this to work, you have to be given the slope, `m`, and at least 1 `(x,y)` point.)
2. If you have the slope, `m`, plug it in for `m` above and pick the `(x,y)` that correspond to the point given.
3. In the equation then, you have the `y`, `m` and `x` known.
4. All you have to do is solve for `b`, the y-intercept.
5. Solve for `b`, then plug in the `b` and `m` into the slope-intercept equation.

WARNING: IF you are not given the slope, then you are given 2 points. Given the 2 points, find the slope `m` with the equation `m=(y_2−y_1)/(x_2−x_1)`, then proceed as in step 2 above.

With this method, you have to solve for b, the y-intercept.

B. Using the point-slope equation (which is a derivation of the slope definition), `(y−y_1)=m(x−x_1)`

1. (Don’t forget, for this to work, you need the slope and 1 point or at least 2 points from which you can find the slope.)
2. (Notice too, that there is NO LONGER a `y_2` and `x_2`, just a `y` and `x`. LEAVE IT THAT WAY!)
3. If you have the slope `m`, use it. If you have 2 points, then find the slope – like the WARNING above.
4. Choose 1 of the `(x, y)` points to use for `(x_1, y_1)` and plug in the values that you know (`x_1`, `y_1`, and `m`).
5. Solve the equation for `y` and remember that you have to distribute on the right side!

With this method you have to you the distribution method on the right. You DO NOT find the `b` or y-intercept.

Either method works, you choose what is most comfortable for YOU!

Here is a link to both methods from purplemath.com.