SOLUTION: Are the following line parallel, perpendicular, or neither? L1 through (9,2) and (3,-8) L2 through (-3,5) and (5, -1)

Algebra ->  Graphs -> SOLUTION: Are the following line parallel, perpendicular, or neither? L1 through (9,2) and (3,-8) L2 through (-3,5) and (5, -1)      Log On


   

Question 93007: Are the following line parallel, perpendicular, or neither?
L1 through (9,2) and (3,-8)
L2 through (-3,5) and (5, -1)
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope of the given two lines.

L1 = (9,2) and (3, -8) The equation of the line with 2 points is given by:

(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)

On substituing for these values we find that

y + 10x - 92 = 0


Similarly find the eqn of the line L2,

8y + 6x - 22 = 0


Now writing both of the equation in the standard form or the slope intercept form, we find the slopes.

First eqn is:

y = -10x + 92 ---------------(1)

Second Eqn is:

+y+=+-%286%2F8%29x+%2B+%2822%2F8%29+

This can be simplified and written as:

+y+=+-%283%2F4%29x+%2B+%2811%2F4%29+ --------------------(2)

WE shall first find the slopes of both the equations.

That is slope of Eqn (1) = -10

And the slope of the Eqn (2) = +%28-3%2F4%29

Two lines are said to be parallel if their slopes are equal and have different y-intercepts.

Two lines are said to be perpendicular if the product of their slopes is equals negative one.

So here in the above example we observe that neither of the above cases hold good for the given two lines.

Hence, they are neither perpendicular nor parallel.

The graph of the above 2 equations look in this way.



Thus the solution
Regards