Perpendicular Lines

Question

Which equation describes the line that passes through the point (– 2, –1) and is perpendicular to the line 4x - 3y =15?
[A] 3x + 4y = –10
[B] 3x + 4y = 10
[C] 4x - 3y = 11
[D] 4x + 3y = –11

Answer 1

The given equation, 4x - 3y =15, is in Standard Form (that is, Ax+By=C).

 

Now, once and forever, convert that to slope-intercept form and find that the slope is (-A/B).  For this problem, the slope is (-4/(-3)) or 4/3.

 

The slope of a perpendicular line is the negative reciprocal of the slope of this line.  So, it is -3/4.  That means that the equation of the perpendicular line, in Standard Form, is 3x + 4y = D, and we need a point to determine D.  The problem gives us the point (-2,-1).

 

3(-2) + 4(-1) = D

  -6 - 4 = D

    -10 = D

 

The equation of the perpendicular line, in Standard Form, is (A) 3x + 4y = -10.

Answer 2

put the original line in slope intercept form

4x - 3y =15

-3y=-4x + 15

y = 4/3x - 5

 

Slope is 4/3, so the perpendicular line must have a slope of -3/4

 

Put all 4 in slope intercept form

A     y = -3/4 x - 5/2            maybe      

B     y = -3/4 x + 5/2           maybe

C     y =  4/3 x - 11/3           nope

D     y = -4/3 x + 11/3          nope

 

Out of A and B, which line goes through (-2, -1)?

A   3x + 4y = -10              B   3x + 4y = 10

   3(-2) + 4(-1) = -10            3(-2) + 4(-1) = 10

   -6  + -4 = -10                     -6  + -4  = 10

         yes                                     no

 

A is your answer

 

Answer 3

We can rewrite the equation of the original ine as 3y =  4x - 15 or y = 4/3 x - 5. Note the slope of this line is 4/3.   The equation of a line perpendicular t0 this one has slope which is the negative reciprocal of the original line or slope = -3/4

 

Noe we are now looking for an equation for the line y = -3/4x + b which goes through (-2,-1)  Substituting into this equation we solve for b 

 

-1  = -3/4 * 2 + b  or b = -1 -3/2 =  -5/2

 

So we have  y = -3/4 x  -5/2  or 4y +3x = -5/2*4  = -10

Answer is 3x + 4y = -10 (A)