SOLUTION: PLEASE HELP SOLVE. DETERMINE WHEATHER THE FOLLOWING IS PERPENDICULAR, PARALLEL OR NEITHER PROBLEM # 1 : 2X+5Y=-8 AND 6+2X=5Y PROBLEM # 2 : 3X=Y AND 2Y-6X=5

Algebra ->  Linear-equations -> SOLUTION: PLEASE HELP SOLVE. DETERMINE WHEATHER THE FOLLOWING IS PERPENDICULAR, PARALLEL OR NEITHER PROBLEM # 1 : 2X+5Y=-8 AND 6+2X=5Y PROBLEM # 2 : 3X=Y AND 2Y-6X=5      Log On


   

Question 57665: PLEASE HELP SOLVE.
DETERMINE WHEATHER THE FOLLOWING IS PERPENDICULAR, PARALLEL OR NEITHER
PROBLEM # 1 : 2X+5Y=-8 AND 6+2X=5Y
PROBLEM # 2 : 3X=Y AND 2Y-6X=5
Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel means the lines have an identical slope (m). Perpendicular means the lines have slopes that are the negative reciprocals of each other (so, if the slope of one line is 2, the slope of its perpendicular line is -1/2). Anything else means the lines intersect at an angle other than 90.
To solve these, write the equations in slope-intercept form and you can solve by inspection.
Problem 1:
eq(1): 2x+5y=-8
eq(2): 6+2x=5y
eq(1) leads to: y=-%282%2F5%29x-%288%2F5%29, so the slope (m) is -2/5
eq(2) leads to: y=%282%2F5%29x%2B%286%2F5%29, so the slope (m) is 2/5
Because the slopes are not the same or the negative reiprocals of each other, they are neither parallel nor perpendicular.
Here is a graph showing them:

The second problem can be solved the same way. The slopes are 3 and 3, which are the same therefore the lines are parallel.