Question

give two examples of parallel lines

Answer 1

Parallel lines are two or more lines that never intersect.  Examples of parallel lines are all around us, in the two sides of this page and in the shelves of a bookcase.  When you see lines or structures that seem to run in the same direction, never cross one another, and are always the same distance apart, there’s a good chance that they are parallel.

 

In algebra, we use something more precise than appearance to recognize and create parallel lines. We use equations.

 

Recognizing Parallel Lines

 

Let’s look at two parallel lines on a graph. 

 



 

 

Line A has an equation of . Line B has an equation of . Can you identify what these two lines have in common?

 

Try comparing the coefficients of x in each equation. They are both 3.  Because the equations are written in slope-intercept form of , the coefficient of x is the slope of the lines. Since both Line A and B have a slope of 3, they have the same slope.

 

We’ve discovered a relationship that is true for all parallel lines—lines are parallel if they have the same slope. Not convinced? Look at the lines on this graph:

 



 

 

The blue lines are parallel—they run in the same direction, keep the same distance apart, and never touch—and they have the same slope. All three red lines share a slope, and they too are parallel to one another. The red and blue lines are clearly not parallel, and they have different slopes.

 

Creating Parallel Lines

 

Now that we’ve learned the relationship between parallel lines, let’s see if we can use that knowledge to create a parallel for a given line.  Remember, parallel lines have the same slope but different [y-intercepts].

Answer 2

The railway track
The side of pages