A graph of an equation in two variables is the set of all points that satisfy the equation.
If you’re given the equation y = 3x-2 and asked to graph it, you would do the following steps. (Note: This equation is a linear equation, which means it will appear as a straight line). The first step is to set up a table of x and y.
y = 3x-2
x |
y |
0 |
-2 |
1 |
1 |
2/3 |
0 |
Assign values to x, then figure out what the value for y will be. For example, if x = 0, then y = -2. If x = 1 then, y = 1, and if x=2/3, then y = 0. Note that it’s good to choose x=0 and y = 0 because x intersects the y-axis when it has the value of 0, and y intersects the x–axis when it has the value of 0.
From the table above, we have the points (0, -2), (1, 1) and (2/3, 0). However, to draw a line you would only need to plot two points and then connect those dots. Since "linear" equations produce a straight line, you might as well use your ruler for this part.
You can see in the graph below these points are connected in a straight line.
Press the "Play Button" on navigation bar to see the steps.
A linear function could be written in the following standard equation y = f(x) = bx+ a. So, a linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. The highest power over the x variable in a linear function is 1.
Example: y = 2x-1 is a straight-line equation, where b=2 and a= -1.
Exercise. Drag Point A and explore how line-equation changes.
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