Algebra 1/Unit 5: Graphing Linear Equations

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Welcome to Week 5 of Speak Math Now! Here, we are going to teach how to graph linear equations. A linear equation is an equation for a straight line. So, when graphing linear equations, the line that we are going to make should match up with our definition, it should be a straight line! Remember this golden rule: The graph of any linear equation in two variables is a straight line. In this lesson, we are going to use three ordered pairs ([x value], [y value])x3 so that we know that we have drawn our line for our equation correctly (2 points (on the rectangular coordinate system) to make a line, and a third point to recheck our line). It may seem quite difficult at a first glance, but as the old saying goes; don't judge a book by its cover.

Without further to explain, let's jump right in!

How do we graph a linear equation?Edit

1st problemEdit

An easy solution for graphing linear equations is two find three points to satisfy an equation, such as 7 + x = y. We can put any number and get an ordered pair that we can graph on the rectangular coordinate system, but for ease, we will pick these small numbers: -1, 0, and 1. Now that we have three numbers to make three ordered pairs, we can go ahead and plug in these x-values into 7 + x = y to get a y-value. Let us see how this goes:

  1. 7 + (-1) = y → y = (-1) + 7 → y = -1 + 7 → y = 6
  2. 7 + (0) = y → y = (0) + 7 → y = 0 + 7 → y = 7
  3. 7 + (1) = y → y = (1) + 7 → y = 1 + 7 → y = 8

We have, through the wonders of math, finally gotten our y-value for our x-value. Now, let's organize them

X-Input Y-Output
(negative)1 6
0 7
1 8

Now that we have organized these numbers, we can go ahead and make the dots (location is according to these 3 ordered pairs) on the rectangular coordinate system:

 
Image represents the ordered pairs: (-1, 6), (0, 7), and (1, 8) graphed

All we need to do is connect the dots and label the line with 7 + x = y, so we know what this line represents. After doing this, your final product of graphing this linear equation should resemble this:

 
Lined and labeled, this is a final product of a graphed linear equation

Hoorah! You've done it! You have just graphed a linear equation, congrats! This is how we do it when it comes to graphing linear equations. Following the rules and procedures detailed here will get you to your established final product that you desire for.


2nd problemEdit

Let us do another one in order for you to remember these procedures. Let us go with the equation: 6 - 20 + x = y. As we did before, let's find three numbers to replace the "x" in this equation with:

  • 3
  • 8
  • 4

Now that we+ have found our pairs, lets calculate these pairs into our equation:

  • 6 - 20 + (3) = y → -14 + 3 = y → -11 = y → y = -11
  • 6 - 20 + (8) = y → -14 + 8 = y → -8 = y → y = -8
  • 6 - 20 + (4) = y → -14 + 4 = y → -10 = y → y = -10

As we did before, we need to make up a chart to organize our new pairs. Here is how your chart should look like:

X-Input Y-Output
3 -11
8 -8
4 -10