Parallel+and+Perpendicular+Lines


 * TASK: Define "parallel"**

You can tell if two lines are parallel by looking at the graph of the lines and by looking at the equation of the lines. On the graph, the two lines **will never intersect.** For example:
 * How do you know if two lines are parallel?**



In the equation, you can tell if two lines are parallel because they have the **exact same slope**. For example:

y = -4x +7 and y = -4x - 2 ARE PARALLEL because they both have a slope of -4

The two lines below are NOT PARALLEL because one has a positive slope and one has a negative slope. Therefore, the lines do not have the exact same slope.


 * IMPORTANT NOTE: If we're using the equation of the line to determine if the lines are parallel, then the equations MUST be in SLOPE-INTERCEPT FORM so that we can easily identify the slope**. If the equations are NOT in slope-intercept form, we must rewrite them in slope-intercept form before we can do anything else with the problem.

**TASK: How do we determine if two lines are parallel by looking at their equations?**

On the Regents, you may be given an equation and asked to identify which equation in the answer choices is parallel to the original equation. For example:
 * What will this look like on the Regents?**

In this problem, we are looking for the line in the answers that has a slope of -4 (because that's the slope of the line in the original problem). Therefore, Answer Choice #1 is the correct answer.

**TASK: Complete the following 4 practice problems:**

1.

2.

3.

4.

On the Regents, there is one exception to how you find parallel lines and that is if the question asks you find a line that is PARALLEL TO THE X-AXIS OR Y-AXIS.
 * THE EXCEPTION:**

If the questions asks for a line parallel to the **x-axis:** That means you're looking for a horizontal line. In a horizontal line, the x-value changes, but the y-value stays constant (see the red line in the image below). It can be anywhere on the graph.



Therefore, when looking for a line that's parallel to the x-axis, we want any answer that says: **y = any number**

If the question asks for a line parallel to the **y-axis,** we're looking for a vertical line where the y-values change, but the x-value stays constant. Therefore, we want any answer that says: **x = any number**

**TASK: Complete the practice problems below.**

1. 2.

3.