Students will graph linear equations using a table.
A linear equation you can plug x vertically… Given an equation that y=_x or x=_y if you substitute values for x or y, and plot a graph it will make a line! The solution to linear equations are ordered pairs for you to use on your graph!
What is a Linear Equation? A linear equation is an equation whose graph forms a straight line. Linear equations are usually shown on a coordinate plane AKA Cartesian Plane Real life situations of linear equations include the stock market as well as the payments of a car.
This is an example of a linear equation y = x + 8 In this case whatever x is plus 8 will give you the value of y
Since the results of a linear equations can be expressed as ordered pairs, the linear equation can be graphed. There are a number of ways to find the solution to a linear equation…for today’s lesson we will look at creating a table of the solutions…
To create a table of solutions to a linear equation do the following: 1. 1. Choose a minimum of 3 values for x 2. 2. Substitute the values of x into the linear equation 3. 3. Simplify to find the value of y 4. 4. Write the solutions as ordered pairs Let’s look at an example…
y = 2x – 1 x y (x, y) 0 y = 2(0) – 1 - 1 (0, - 1) 1 y = 2(1) – 1 1 (1, 1) 2 y = 2(2) – 1 3 (2, 3) 1. Choose a minimum of 3 values for x 2. Substitute the value of x into the equation 3. Simplify to determine the value of y 4. Write as an ordered pair
How do you choose the value of x? You can use any number for the value of x…however, you can make your life easy by choosing -1, 0, and 1, because you can do mental math and they are easy to graph. You choose a minimum of 3 numbers because when graphed the expected result is a straight line. If you don’t get the straight line, then you have to go back and check your calculations… x0 1 2
Use the ordered pair from the table to graph the linear equation. Again…when graphing the result should be a straight line… Any point (ordered pair) on that line will be a solution to the linear equation…
(x, y) (0, - 1) (1, 1) (2, 3) x y (0, -1) (1,1) (2,3) y = 2x – 1
Find 3 different ordered pairs that are the solutions to the equation 1.y = 3x – 5 2.y = -2x – 6 3.y = ½ (4 – 2x) 4.y = 4( ½ x – 1)
Once you get the hang of it…this concept is really easy…. However, like everything else to become proficient you will need to practice… It’s ok if you make a mistake…you can fix it… The goal here is to keep an open mind and try…