Write an equation of the line that passes through the point (-4,-1) and is (a) parallel to and (b) perpendicular to the line 2x+7y=14

Question

Please help i am vert stuck

Answer 1

The given line is 7y  = 14 - 2x

 

                            y = 2 - (2/7)x

 

                                = (-2/7)x + 2

 

 THe given line has slope (-2/7)

 

 

 

Parallel lines have the same slope:

 

M=-2/7 and (-4,-1) ---> X = -4 and y = -1

 

  B = y - Mx = -1 - (-2/7)(-4) = -1 - (8/7) = -15/7

 

  y = (-2/7)x - 15/7

 

 

Perpendicular lines have slopes that are NEGATIVE reciprocals.

The slope of the perpendicular line is (7/2)

 

 

M = 7/2,  (-4,-1) ---> x = -4 and y = -1

 

 B = y - mx = (-1) - (7/2)(-4)

                   = -1 + 14 = 13

 

 y = (7/2)X + 13

Answer 2

(a)

 

If parallel, the slopes must be the same.

 

m = -a/b = -2/7

 

In point-slope form, the equation is

 

y - y₁ = m(x - x₁)

 

y - (-1) = (-2/7)[x - (-4)]

 

y + 1 = (-2/7)(x + 4)

 

(b)

 

Solve the same way as part (a), but this time the slope is

 

m' = -1/m = -1/(-2/7) = 7/2

 

y + 1 = (7/2)(x + 4)