Day 100 thru 102 – February 2, 3, 4

Algebra 1a: 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 ${\displaystyle (x,y)}$ or 1 point ${\displaystyle (x,y)}$ and the slope, ${\displaystyle m}$ 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, ${\displaystyle y=mx+b}$

1. (Don’t forget, for this to work, you have to be given the slope, ${\displaystyle m}$, and at least 1 ${\displaystyle (x,y)}$ point.)
2. If you have the slope, ${\displaystyle m}$, plug it in for ${\displaystyle m}$ above and pick the ${\displaystyle (x,y)}$ that correspond to the point given.
3. In the equation then, you have the ${\displaystyle y}$, ${\displaystyle m}$ and ${\displaystyle x}$ known.
4. All you have to do is solve for ${\displaystyle b}$, the y-intercept.
5. Solve for ${\displaystyle b}$, then plug in the ${\displaystyle b}$ and ${\displaystyle m}$ 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 ${\displaystyle m}$ with the equation ${\displaystyle m=\frac{y_2-y_1}{x_2-x_1}}$, 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), ${\displaystyle (y-y_1)=m(x-x_1)}$

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 ${\displaystyle y_2}$ and ${\displaystyle x_2}$, just a ${\displaystyle y}$ and ${\displaystyle x}$. LEAVE IT THAT WAY!)
3. If you have the slope ${\displaystyle m}$, use it. If you have 2 points, then find the slope – like the WARNING above.
4. Choose 1 of the ${\displaystyle (x,y)}$ points to use for ${\displaystyle (x_1,y_1)}$ and plug in the values that you know (${\displaystyle x_1}$, ${\displaystyle y_1}$, and ${\displaystyle m}$).
5. Solve the equation for ${\displaystyle y}$ 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 ${\displaystyle b}$ or y-intercept.

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

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

Two of tonight’s homework problems solved by MrE are here! Just click it!