Write the equation of the line parallel to the line

Question

(a) Write the equation of the line parallel to the line 3x + 1 = −2y and through the midpoint of the segment that joins (2, 3) and (−4, −3).

 

(b) Equation of the line perpendicular to the lines in (a) and passing through the point (−3, −1).

Answer 1

a)

Find the midpoint of (2,3) and (-4, -3):

 

(2 + (-4), 3 + (-3))

 

 

So through

(-2, 0) 

and parallel to:

3x+1 = -2y

 

or y = -3x/2 -1/2

 

Slope = m = -3/2

 

y-0 = -3/2(x - (-2))

 

y = (-3/2)(x+2)

 

y = (-3/2)x - 3

 

 

b)

 m of perpendicular line is -1/(-3/2) = -1(-2/3) = 2/3

 

Point is (-3, -1)

 

y - (-1) = (2/3) (x - (-3))

 

y + 1 = (2/3) (x + 3)

 

y = (2/3)x + 2 - 1

 

y = (2/3)x + 1