The Standard Form of a Linear Equation

We have learned about two different types of equations for lines, slope-intercept form (y=mx+b) and point-slope form (y-y1=m(x-x1). Now we are going to learn about standard form. Standard form of an equation is Ax + By = C.

We can write equations in standard form by moving variables or constant terms, similar to what we would do if we were solving equations. Here is an example:

y = 2x - 9

If I subtract 2x from both sides then I get -2x + y = -9. Now we have an equation in standard from. Remember in class that we also discussed that we do not want fractions or decimals in our answer. We can eliminate fractions by multiplying everything in the equation by the denominator of the fraction; or, if we are dealing with decimals we can move the decimal the same amount of places to make sure that every number is whole.

We might also be given just a little information and have to use it to write an equation and then rewrite it in standard form. Here's an example:

(-8 , 3), m = 2

We can use this information to write an equation in point-slope form:

y - 3 = 2(x + 8) Do the distributive property
y - 3 = 2x + 16 Move the -3 to the other side
y = 2x + 19 Move the 2x to the other side

Answer: -2x + y = 19

Finally we discussed vertical and horizontal lines. An equation of a vertical line is always in x= form and a horizontal line is always in y= form. If we are given a point and they ask us to write an equation of a horizontal and vertical line here is what we will do:

(-4 , 4)

x = -4 Vertical line because the value of x in the coordinate is -4.
y = 4 Horizontal line because the value of y in the coordinate is 4.

I hope this has helped, let me know if you have questions.

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.

Welcome To Online Algebra

Welcome to our Algebra I class "blog". For those of you new to blogging, this is a way for us to communicate after class time for help on homework. Why do we need a class blog? Well, I am glad you asked. Many of you have mentioned the fact that you understand homework in class but not when you get home. "It is easier, when you do it on the board" is a common phrase I hear from you all. So, with the help of technology, my goal is to provide additional help, notes, examples, etc., to aid in our homework endeavors.

Each day, I plan to post our lesson so you can refresh your memory when you are at home doing your homework. You will also be able to post a question (comment) that I can receive and reply additional help. This is a trial run, so let's see how helpful it really is.