Problem 1 Checking for Parallel Lines

Are lines l 1 l sub 1  and l 2 l sub 2  parallel? Explain.

• Step 1 Find the slope of each line.

  slope of  l 1 = 5 − ( − 4 ) − 1 − 2 = 9 − 3 = − 3 slope of  l 2 = 3 − ( − 4 ) − 3 − ( − 1 ) = 7 − 2 = − 7 2 table with 2 rows and 2 columns , row1 column 1 , slopeof . l sub 1 , column 2 equals . fraction 5 minus . open , negative 4 , close , over negative 1 minus 2 end fraction . equals , 9 over negative 3 , equals negative 3 , row2 column 1 , slopeof . l sub 2 , column 2 equals . fraction 3 minus . open , negative 4 , close , over negative 3 minus . open , negative 1 , close end fraction . equals , 7 over negative 2 , equals negative , 7 halves , end table

• Step 2 Compare the slopes.

  Since − 3 ≠ − 7 2 , l 1 negative 3 not equal to negative , 7 halves , comma , l sub 1  and l 2 l sub 2  are not parallel.

✓ Got It?

1. Line l 3 l sub 3  contains A ( − 13 , 6 ) eh open negative 13 comma 6 close  and B ( − 1 , 2 ) . b open negative 1 comma 2 close .  Line l 4 l sub 4  contains C(3, 6) and D(6, 7). Are l 3 l sub 3  and l 4 l sub 4  parallel? Explain.

Problem 2 Writing Equations of Parallel Lines

What is an equation of the line parallel to y = − 3 x − 5 y equals , minus 3 x minus 5  that contains ( − 1 , 8 ) ? open negative 1 comma 8 close question mark

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✓ Got It?

2. What is an equation of the line parallel to y = − x − 7 y equals , minus x minus 7  that contains ( − 5 , 3 ) ? open negative 5 comma 3 close question mark

Take Note Key Concept: Slopes of Perpendicular Lines

• If two nonvertical lines are perpendicular, then the product of their slopes is − 1 . negative 1 .
• If the slopes of two lines have a product of − 1 , negative 1 comma  then the lines are perpendicular.
• Any horizontal line and vertical line are perpendicular.