Graphing Linear Equations by Creating a Table of Coordinates

In this video we look at how to graph the equation y = 2x + 3. This is a linear equation, since when it is graphed it will form a straight line. The video provides a detailed explanation of how to graph the solution by first creating a table of coordinates.

 
 
Morgan

Your Turn:

Morgan had $x$ dollars at the beginning of the day. He spent $y$ dollars on clothes. At the end of the day he had $5% dollars left. Write an equation to represent this situation and create a graph to show the possible values for the amount he had at the start and how much he spent.

Solution:

The equation to solve this is $\color{blue}{x-y=5}$.
Because Morgan did not spend more than he had all the solutions will have to be positive, and the graph will be in quadrant I.

Lets start by making a table.
$$
\begin{array}{c|c|c|c}
x & x-y=5 & y & \color{blue}{(x,y)}\\
\hline
20 & 20-y=5 & 15 & \color{blue}{(20,15)}\\
\hline
30 & 30-y=5 & 25 & \color{blue}{(30,25)}\\
\hline
35 & 35-y=5 & 30 & \color{blue}{(35,30)}\\
\hline
48.50 & 48.50-y=5 & 43.50 & \color{blue}{(48.50,43.50)}\\
\hline
\end{array}
$$

Remember: if you choose a value for one of the variables, you can determine the value of the other, and since there are an infinite number of choices for x, there will be an infinite number of solutions.

graphing the linear equation- x - y = 5

What do the coordinates (0,5) represent?