Question

Which equation represents the line that is perpendicular to y=1/4 and passes through (-6,-9)?

Answer 1

`\displaystyle \boxed{y = -4x - 33}`

Explanation:

`\displaystyle y = (1)/(4)x`**

Now, perpendicular equations have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so
`\displaystyle (1)/(4)`becomes −4 and you do the following:

−9 = −4[−6] + b

24

`\displaystyle -33 = b \\ \\ y = -4x - 33`

I am joyous to assist you at any time.

Answer 2

perpendicular means

m1 = 1/4

m2= -1/(1/4)

= -4 (Perpendicular slope)

(-6,-9) = (x1,y1)

so,

y-y1 = m (x-x1)

y-(-9)= -4 (x-(-6))

y+6 = -4 (x+6)

y+6 = -4x-24

y= -4x-24+6

y= -4x-18

hope it helps ^°^