Problem 1 Finding Slope

What is the slope of the line that passes through the given points?

1. ( − 3 , 7 ) open negative 3 comma 7 close  and ( − 2 , 4 ) open negative 2 comma 4 close

   m = y 2 − y 1 x 2 − x 1 = 4 − 7 − 2 − ( − 3 ) = − 3 1 m equals . fraction y sub 2 , minus , y sub 1 , over x sub 2 , minus , x sub 1 end fraction . equals . fraction 4 minus 7 , over negative 2 minus . open , negative 3 , close end fraction . equals , negative 3 over 1

   The slope of the line that passes through ( − 3 , 7 ) open negative 3 comma 7 close  and ( − 2 , 4 ) open negative 2 comma 4 close  is − 3 1 negative 3 over 1  or − 3 . negative 3 .

   Think

   Does it matter which point you choose for ( x 1 , y 1 x sub 1 , comma , y sub 1 )?

   No; you can choose either point for ( x 1 , y 1 ) . x sub 1 , comma , y sub 1 , close .

2. (3, 1) and ( − 4 , 1 negative 4 comma 1 )

   m = y 2 − y 1 x 2 − x 1 = 1 − 1 − 4 − 3 = 0 − 7 = 0 m equals . fraction y sub 2 , minus , y sub 1 , over x sub 2 , minus , x sub 1 end fraction . equals . fraction 1 minus 1 , over negative 4 minus 3 end fraction . equals , 0 over negative 7 , equals 0

   The slope of the line that passes through (3, 1) and ( − 4 , 1 ) negative 4 comma 1 close  is 0 − 7 0 over negative 7  or 0.

3. ( 7 , − 3 7 comma negative 3 ) and (7, 1)

   m = y 2 − y 1 x 2 − x 1 = 1 − ( − 3 ) 7 − 7 = 4 0 m equals . fraction y sub 2 , minus , y sub 1 , over x sub 2 , minus , x sub 1 end fraction . equals . fraction 1 minus . open , negative 3 , close , over 7 minus 7 end fraction . equals , 4 over 0

   Division by zero is undefined, so slope is undefined for the line that passes through ( 7 , − 3 ) open 7 comma negative 3 close  and (7, 1).

✓ Got It?

1. What is the slope of the line that passes through the given points?
   1. (5, 4) and (8, 1)
   2. (2, 2) and ( − 2 , − 2 negative 2 comma negative 2 )
   3. (9, 3) and ( 9 , − 4 ) open 9 comma negative 4 close
   4. Reasoning Use the slope formula to show in part (a) that it does not matter which point you choose for ( x 1 , y 1 ) . x sub 1 , comma , y sub 1 , close .

Take Note Concept Summary: Slope of a Line

Image Long Description