parallel lines & perpendicular lines

Question

Problem is : Without graphing , determine which of the following equations are parallel to each other . which represents perpendicular lines 

 

A)-3x+y=5    B) -5x+y=3

 

C)x+5=-15.   D) -15x+5y=-25

Answer 1

Hi Briana

 

Recall that parallel lines have the same slope and perpendicular line have slopes that are the negative inverse of the other.

 

So.

 

A) -3x+y=5

I find it best to restate the equation in the slope intercept form.

y = 3x+5

Slope = 3

 

B) -5x+y=3

y = 5x + 3

Slope = 5

 

C) x+5 = -15

Is it possible that this should be x+5y = -15? 

If so,

5y = -x-15

y = -x/5 -3

slope = -1/5

 

D)  -15x+5y = -25

5y = 15x - 25

y = 3x-5

slope = 3

 

Since A) and D) have the same slope (+3) those lines are parallel.

Since the slope of B) is 5 and the slope of C) is -1/5, the negative inverse, those lines are perpendicular.

Answer 2

the parallel lines have equal slopes with same orientation, i.e., same sign if the equation in standard form: y=mx+c

the perpendicular lines have slopes reciprocal in value and opposite in sign.

So converting all the equations in standard form,

A)-3x+y=5

=>y=3x+5

B) -5x+y=3

=>y=5x+3

C)x+5=-15

=>x+20=0.y

=>y=x/0+20/0,  the slope is undefined because the line has no Y-axis intercept; this line is parallel to Y-axis with X-axis intercept equal to 20

D) -15x+5y=-25

=>-3x+y=-5

=>y=3x-5 has a slope that is equal is value and same in sign as that of the line represented by A) hence they are parallel

 

Answer 3

Hi Briana,

Rewrite the equations in the form y = mx + b , then if 

(1)two of the equations have the same m values then they are parallel

(2)the product of the two m equals -1 then they are  perpendicular

 

A) -3x +y = 5,    y = 3x +5

B) -5x +y = 3,    y = -5x +3

C) x+5 =15 ???

D) -15x +5y =-25, y = 3x - 5

 

A and D are parallel, 

WHAT IS THE EQUATION IN (C)?