consider the line x-5y=-2

Question

Find the equation of the line that is perpendicular to this line and passes through the point
, −3− 5
.

Find the equation of the line that is parallel to this line and passes through the point
, −3− 5
.

Answer 1

convert to point intercept form:

x-5y=-2

y =(2+x)/5

y = 2/5+x/5

y = (1/5)x + 2/5

 

Perpendicular line take the negative inverse of m

m = 1/5

-m^-1 = -5

 

therefore the new equation is

y = -5x + 2/5  

 

we can disregard the "2/5" for this problem

 

y-(-5) = (-5)(x-(-3))

y+5 = -5x-15

y =-5x-20 (this is the new perpindicular equation) 

 

as for the parallel please double check you question by definition, a parallel line cannot go through the same point, but if you are looking of the parallel line through the original equation:

 

 

y = (1/5)x + 2/5

y-(-5) = (1/5)(x-(-3))

y+5 = x/5 +3/5

y = x/5 + 3/5 - 5

y = x/5 - 4_2/5 => y = x/5 - 22/5 => y = (x-22)/5

 

I hope this explanation helps!

Answer 2

Hi  Katherine

 

The first step to do is leave the variable y in one side and move other terms to the other side of the "=" symbol:

 

x - 5y = -2

 

-5y     = -2 - x  (after multiplying by -1 both sides)

 

  5y    = x + 2

 

    y    = x/5 + 2/5   (after dividing by 5 both sides)

 

The second step is to estimate the slope of the perpendicular line:

 

    y  =  x/5  +2/5         Have a slope  m = 1/5

 

The line perpendicular y⊥ has the following expression:

 

    y⊥   =  (-1/m)x  + b       where m is 1/5

 

    y⊥ = -5x + b     

 

 

Because the ordered point (-3,-5) belongs to this perpendicular line, you have:

 

     -5   =  (-5)*(-3)  + b

 

     -5   =  15  +  b    ⇒     b  = -5 - 15     ⇒   b = -20

 

Solution:   The perpendicular line is :  y⊥  = -5x  - 20

Answer 3

First, convert the equation to slope intercept form.

x - 5y = -2

-x            -x     subtract x 

    -5y = -x - 2

     ___   _____ divide by -5

       -5      -5

 

y = 1/5 x + 2/5      (slope: 1/5    y-intercept: 2/5

 

FIND THE PERPENDICULAR LINE PASSING THROUGH (-3,-5)

The slope of the original line is 1/5, but a perpendicular line would have a slope that is the negative [opposite] inverse. The slope you need is -5.

To find the line that goes through (-3,-5), you need to find the y-intercept, or "b".

 

Use slope=-5 and y=-5 and x=-3 in the slope intercept formula to find b.

y   =  mx   + b

-5 = -5(-3) + b

-5 =  15 + b

-15   -15        subtract 15 from both sides to solve for b

-20= b

 

Now you have the slope (m=-5) and y-intercept (b=-30) and can create the equation using y=mx+b

y = -5x + -20

 

 

FIND THE PARALLEL LINE PASSING THROUGH (-3,-5)

This works the same way, except for the slope. Two parallel lines have the same slope, therefore m=1/5.

 

Use slope=1/5 and y=-5 and x=-3 in the slope intercept formula to find b.

y = mx + b
  -5 =  1/5(-3) + b
  -5 = -3/5 + b
+3/5  +3/5    add 3/5 to both sides to solve for b
-4 2/5 = b

Now you have the slope (m=-5) and y-intercept (b=-30) and can create the equation using y=mx+b
y = 1/5x + -4 2/5