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

Answer:

y = 4(x) - 12

explanation:

$\sf y=-\dfrac{1}{4} x -8$

$\sf Here \ the \ gradient \ is -\dfrac{1}{4}$

$\sf If \ perpendicular: \ \sf -\dfrac{1}{m} \rightarrow -\dfrac{1}{-\dfrac{1}{4}} \rightarrow 4$

Find equation of line perpendicular to this line:

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

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

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

Answer 2

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!