A Mathematical Question...?

Question

A Line L1 has equation y = 2x + 5
Line L2 has equation 3x + py =14

Find the value of p in the case where

Q1 :L1 is parallel to L2

and

L1 is perpendicular to L2...

This Is NOT my homework!

Answer 1

First, solve for y:

3x + py = 14
py = -3x + 14
y = -3x/p + 14/p

Q1: since the equation has a slope of 2, a parallel line will have the same slope. In order for the coefficient of x to be 2, p must be -1.5

Q2: Perpendicular lines have negative inverse slopes. This means that a line perpendicular to the first line would have a slope of -½. In order for the slope to be -½, p must be 6.

Answer 2

For line 1 the slope is 2 and for line 2 the slope is (-3/p).If L1 is perpendicular to L2 then {2 * (-3/p))}= -1 gives p = 6. When the two lines are parallel they have the same slope i.e. (-3/p)=2 which implies p = (-3/2).[Remember you have to express the equations of the lines in the form y=mx+c, where m is the slope of the straight line. In case of parallel lines the slopes are equal and in case of perpendicular lines the product of the slopes of the lines is -1]

Answer 3

First, express both in the form y = mx + b

L1: y = 2x + 5

L2: y= -3x + 14 => y = -(3/p)x + 14/p

Q1: parallel means that slope=m is the same
So, 2= -(3/p) => p= -3/2

perpendicular means the slopes are negative reciprocals
So, 2= p/3 => p=6

Done!

Answer 4

solve the second equation for y
if the lines are parallel m1=m2
if the lines are perpendicular, m1= -1/m2

L2 is rewritten y=-(3/p)x + 14/3
for the lines to be parallel, 2 = -3/p or p=-1.5
for the lines to be perpendicular, 1/2 = 3/p or p= 6