Question

1) Find the equation of the line that is perpendicular to y=-1/4x - 8 and passes though the point (2,-4).

A) y=4x-12
B) y=4x+4
C) y=1/4x-12
D) y=1/4x+4​

Answer 1

Y=4x - 12

Step-by-step explanation:

y=mx + c

m means gradient

m1 x m2 = - 1

-1/4 x 4 = 4

(your finding the reciprocal)

(x=2, y=-4)

Second line has a gradient of 4, substitute (2,-4) into:

Y = 4x + c

-4 = 4x2 + c

-4 = 8 + c

-8

-12 = c

Thus, y=4x - 12

Hope this helps!

Answer 2

y = 4(x) - 12

Step-by-step explanation:

`\sf y=-(1)/(4) x -8`

`\sf Here \ the \ gradient \ is -(1)/(4)`

`\sf If \ perpendicular: \ \sf -(1)/(m) \rightarrow -(1)/(-(1)/(4)) \rightarrow 4`

Find equation of line perpendicular to this line:

`\rightarrow \sf y - -4 = 4 ( x -2)`

`\rightarrow \sf y +4 = 4 x -8`

`\rightarrow \sf y = 4 x -12`