SOLUTION: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-8y=-18 32x+12y=-18

Algebra ->  Linear-equations -> SOLUTION: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-8y=-18 32x+12y=-18       Log On


   

Question 187407: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
3x-8y=-18
32x+12y=-18
Found 2 solutions by checkley77, solver91311:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
3x-8y=-18
-8y=-3x-18
y=-3x/-8-18/8
y=3x/8-9/4 (red line)
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32x+12y=-18
12y=-32x-18
y=-32x/-12-18/-12
y=8x/3+3/2 (green line)
the slopes are: 3/8 & 8/3 which says they are neither parallel nor perpendicular.
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+3x%2F8+-9%2F4%2C+8x%2F3+%2B3%2F2%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 3x/8 -9/4 and 8x/3 +3/2).

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




and



So, calculate the slopes. Since both equations are in standard form, i.e.

,

you take the opposite of the coefficient on x, which would be -3 in the case of your first equation, and divide it by the coeffiecient on y, which would be -8 in the case of your first equation. Do the same thing for your second equation. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular. If there is any other relationship between the slopes, then the lines are neither parallel or perpendicular.

John