Day 59

Algebra: Chapter 7-6, p 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:

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.
6. If you don’t have the slope, then you have 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 step 6 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 purplemat.com.

Math 8: Chapter 5-5, p 244

Adding and Subtracting Unlike Fractions

Remember, to add or subtract fractions, we have to find the least common denominator (LCD). Sometimes, it just easy to multiply both denominators to find the LCD. BUT, it depends, their might be something smaller that is common to both denominators.