How to find out how slopes are perpendicular, parallel, or neither. Please help me I missed the whole lecture retaking a quiz!

Question

math slopes linear equations perpendicular parrellel

Answer 1

Wow. Here is the easy version:

 

If two lines are parallel, they have the same slope.

 

EX - y=1/4x - 1 and y=1/4x + 7 are both parallel

 

If two lines are perpendicular, the slopes will have these two conditions - 1) Change the sign and 2) "Flip" the slope (reciprocal).

 

EX - y=-1/4x - 1 and y=4x - 1 are both perpendicular

 

If the slopes are ANYTHING else, the lines are neither parallel nor perpendicular

Answer 2

Hi Savannah,

 

       I you have two lines y₁=m₁x+b₁ and y₂=m₂x+b₂  then the two lines are parallel if m₁=m₂ for example if   

y₁=2x+8 and y₂=2x+10 are parallel. m₁=2 and m₂=2

The two lines are perpendicular when m₁*m₂=-1 an example of this would be y₁=7x+2 and y₂=-(1/7)x+14 here m₁*m₂=(7)(-1/7)=-1.

 

Hope this helps you

Jim

 

 

Answer 3

Two lines on the coordinate plane can:

1. intersect in one point, with different slopes;

2. lie on top of each other, so really the same line with the same equation, and so the same slope; or

3. have no points in common, so are parallel with the same slope.

If the two lines intersect in one point (case 1), they can form right angles and be perpendicular. Here's how: http://www.wyzant.com/resources/files/264519/perpendicular_lines_slope_relationship_proof

=====

Most states have now adopted the Common Core Standards for K-12 subject requirements.

http://www.corestandards.org/Math/Content/HSG/CO/
CCSS.Math.Content.HSG.CO.A.1:
“Know precise definitions of … perpendicular line, parallel line …”

“Precise definitions” from Glencoe, Geometry, 2005:
pg. 40: “Lines that form right angles are perpendicular.”
pg. 126: “Coplanar lines that do not intersect are called parallel lines”.

“Precise definitions” from Euclid’s Elements:
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html#defs:
“Definition 10. When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.”
“Definition 23. Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.”

http://www.corestandards.org/Math/Content/HSG/GPE/
CCSS.Math.Content.HSG.GPE.B.5:
“Prove the slope criteria for parallel and perpendicular lines … .”

The slope criteria IS NOT the definition of parallel or perpendicular lines.

If two linear equations have the same graph and you want to think of the situation as two lines lying on top of each other, then they are NOT PARALLEL BECAUSE THEY MEET IN AN INFINITE NUMBER OF POINTS.

Answer 4

first you have to know the definition of a  slope:

 

   Difference in Y - coordinates of of 2 points  Over difference of X coordinates of the same 2 points.

 

        Given 2 points of a line  A ( X_1, Y _{1 ) , B} ( X_2, Y 2).

 

      Slope = m = ( Y₂ - Y₁ ) / ( X₂ - X_{1 )}

 

             The main feature of line is that slope between any2 points of the line has equal values .

 

                This property of a line makes the equation ( relationship between Y- coordinates  and

               

               X -ccordinates ) to be

 

              Y = mx + b   / m is slope and b is the coordinate of Y -intercept.

 

              Two lines with equations of :

                                                        L1 : Y = m1 X + b!

 

                                                        L2 : Y : m2 X + b2

 

                L1 & L2 are parallel if and only if   m1= m2

 

                L1 & L2 are perpendicular if and only if m1 = - 1/ m2/