Writing Linear Equations Given Two Points

As we talked about in class, there is nothing new to learn in this section. We just taking what we already know and putting it into one problem. Remember that we are writing our questions in slope-intercept form: y=mx+b. First we wrote equations given the slope (m) and the y-intercept (b); with this information we just had to plug the m and b into the equations. Next we were given the slope and a point, where we had to plug the slope and point into the equations to solve for b so that we could write a new questions. Today we will only be given 2 points. We will have to use these points to find the slope and then use the slope and a point to find the y-intercept.

Here's how! Remember the equation for finding slope...that's right...

y2 - y1
x2 - x1

So we plug our points into the equation and solve for m. Once we know the slope we can take one of the two points...Does it matter which point we choose?...No it doesn't, just pick one the the points and plug it into the y=mx+b formula to solve for b (this is what we did the night before). Finally, we know the slope and we know the y-intercept, we can now plug those pieces of information into the equation and we get our answer.

Here is an example:

(5 , 3) & (4 , -3)

First we must find the slope, we have the formula for slope so let's plug it into the equation...

-3 - 3 = -6
4 - 5 = -1

So, our slope is 6 or 6/1.

Next we must pick a point and find the y-intercept, I am going to use the point (5 , 3) because I don't want to deal with negatives (remember, it does not matter which point I choose)...

3 = 6(5) + b
3 = 30 + b

Now we have a one-step equations to solve for b.

b = -27

I know my slope and I know my y-intercept, all I have to do now is plug them into the slope-intercept form of an equation.

y=6x - 27

That's my answer, that's all there is, and these steps will only work....everytime.

I hope this has helped. If you have specific questions post a comment and I will TRY and get it answered, so check back later for my replies.