Hi,

 parallel (lines slant in same direction):Slopes identical

perpendicular: Slopes are negative reciprocals of one another

Neither: slopes do not satisfy either of the above:

4x+8y=16  OR y = (-1/2)x + 2    m = -1/2

3x+6y=7   OR y = (-1/2)x + 7/6  m = -1/2

These lines are Parallel, their slopes are identical

 

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 I would like to know how to determine if the 2 lines are parallel, perpendicular or neither, how do I apply the formula, I always forget;



4x+8y=16

3x+6y=7

-----------

Solve for y

4x+8y=16

y = (-1/2)x + something

Slope = -1/2

---------

3x+6y=7

y = (-1/2)x + something

Slope = -1/2

-------------

The slopes are equal, -1/2, so they're parallel.

---------------

PS  The "somethings" are the y-intercepts.  They're not relevant in finding the slopes, but if they're equal, then it's the same line.

That's called the slope-intercept form, y = mx + b

 

Answer by poliphob3.14(115)   (Show Source): You can put this solution on YOUR website!
 First you have to write equations in the slope-intercept form:.



Second you have to find the slopes:1) If  the lines are parallel.



2)If  the lines are perpendicular.



Let solve our problem:, written in slope-intercept



form is:, since,  



thus, the lines are parallel.



 

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