GOAL:To understand and graph linear equations of two variables
The graph of an equation with two variables is the collection of all points (x,y) that are solutions to the equation.
There are an infinite number of solutions to an equation of the form Ax+By=C, therefore the graph of this equation is a line.
Given an equation, y=3x+5, what are the solutions to this equation?
We can begin by constructing a table using Microsoft Excel:
| x | y=3x+5 |
| -3 | -4 |
| -2 | -1 |
| -1 | 2 |
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| 3 | 14 |
This gives us a list of some of the solutions to the equation in ordered pair form.
We can now check this graph to see that the solutions we found are present.
EXTENSION: What will happen to the graph of y=3x+5 if we change the constant?
HINT: Try graphing y=3x+n using graphing calculator and animating the graph.
Determine the solutions to the equation y=-(1/2)x+2 and show the graph.
1. We can use Microsoft Excel to develop a spreadsheet that will help us determine what the solutions to the eqwuation are.
2. We can then use graphing calculator to show the graph of the line.
3. We can then check to see that our solution set is represented in the resulting graph.
Determine the solution set for y=x and y=-x.
Show the each graph on the same axis.
What do you notice about the two graphs?