Objective:
To graph horizontal and vertical lines.Vocabulary:
- Horizontal - goes left to right (think horizon)
- Isolate - get it by itself (alone).
- Vertical - goes up and down.
Notes:
- The graph of x = a is a vertical line that goes through point a on the x-axis.
- The graph of y = b is a horizontal line that goes through point b on the y-axis.
Examples:
1. Sketch the graph of x = 3.
When we graph in a coordinate plane we have two variables, x and y. For the equation x = 3, x is ALWAYS 3. It doesn't make any difference what y is, x can only be 3.
The equation, x = 3, doesn't tell us anything about y. It doesn't restrict y at all, so y can be any number.
Plot a few points making each x-coordinate 3 and varying the y-coordinate. Some examples are (3, −4), (3, −1), (3, 2), and (3, 5).
Draw a line with arrows through the points you plotted. Make sure to label the line.
2. Sketch the graph of y = −4.
For the equation y = −4, y is ALWAYS −4. It doesn't make any difference what x is, y can only be −4.The equation y = −4 doesn't tell us anything about x. It doesn't restrict x at all, so x can be any number.
Plot a few points with the y-coordinate always -4, and vary the x-coordinate. Some examples are (−4, −4), (−2, −4), (0, −4), and (3, −4).
Draw a line with arrows through the points you plotted. Make sure to label the line.
Hint:
Graphing these types of problems is easy if you remember the following:- If the problem is x = __ then it cuts through the x-axis.
- If the problem is y = __ then it cuts through the y-axis.