SOLUTION: Write an equation of a line (a) parallel to and (b) perpendicular to the line 2x+3y=-6 and containing the point (-4, -5). I know that the slope for (a) is -2x/3 and the slope fo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Write an equation of a line (a) parallel to and (b) perpendicular to the line 2x+3y=-6 and containing the point (-4, -5). I know that the slope for (a) is -2x/3 and the slope fo      Log On


   

Question 987513: Write an equation of a line (a) parallel to and (b) perpendicular to the line 2x+3y=-6 and containing the point (-4, -5).
I know that the slope for (a) is -2x/3 and the slope for (b) is 3x/2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2x+%2B+3y+=+-6+
+3y+=+-2x+-+6+
+y+=+-%282%2F3%29%2Ax+-+2+
-------------------
Any parallel line has slope = +-2%2F3+
Any perpendicular line has slope = +-1%2Fm+=+3%2F2+
-------------------
( -4,-5 )
(a)
Use general point-slope formula
+%28+y+-%28-5%29+%29+%2F+%28+x+-%28-4+%29+%29+=+-2%2F3+
+%28+y+%2B+5+%29+%2F+%28+x+%2B+4+%29+=+-2%2F3+
+3%2A%28+y+%2B+5+%29+=+-2%2A%28+x+%2B+4+%29+
+3y+%2B+15+=+-2x+-+8+
+3y+=+-2x+-23+
+y+=+-%282%2F3%29%2Ax+-+23%2F3+
-------------------------
(b)
+%28+y+-%28-5%29+%29+%2F+%28+x+-%28-4+%29+%29+=+3%2F2+
+%28+y+%2B+5+%29+%2F+%28+x+%2B+4+%29+=+3%2F2+
+2%2A%28+y+%2B+5+%29+=+3%2A%28+x+%2B+4+%29+
+2y+%2B+10+=+3x+%2B+12+
+2y+=+3x+%2B+2+
+y+=+%283%2F2%29%2Ax+%2B+1+
-------------------
check:
(a)
(-4,-5)
+y+=+-%282%2F3%29%2Ax+-+23%2F3+
+-5+=+-%282%2F3%29%2A%28-4%29+-+23%2F3+
+-5+=+8%2F3+-+23%2F3+
+-15%2F3+=+-15%2F3+
OK
(b)
(-4,-5)
+y+=+%283%2F2%29%2Ax+%2B+1+
+-5+=+%283%2F2%29%2A%28-4%29+%2B+1+
+-5+=+-6+%2B+1+
+-5+=+-5+
OK