Question

What is the equation of the line that passes through the point (-2,14) and is perpendicular to the line with the following equation?
y = - 2/5x -1

a. y = -5/2x + 9

b. y = -2/5x + 16

c. y = -2/5x + 12

d. y = 5/2x + 19

Answer 1

Answer:

(d). y = $\frac{5}{2}$ x + 19

Step-by-step explanation:

Slope of perpendicular lines are opposite reciprocals.

The given equation is y = $-\frac{2}{5}$ x - 1 and slope of this equation is $-\frac{2}{5}$

Slope of perpendicular line to the given line is $\frac{5}{2}$

There is only one option (d). where is slope $\frac{5}{2}$

Thus, the answer is (d). y = $\frac{5}{2}$ x + 19

Let plug in the coordinates of given points, just to check that we choose the correct answer:

14 = $\frac{5}{2}$ * (- 2) + 19

14 = 14

Done!!!

Answer 2

Answer:

y = -2/5x-2

y(5x-1)=-2

5x -1= y(-2)

5x-1=-2y

5x+2y-1=0

(ax+by+c=0)

a=5 b=2 c=-1

perpendicular distance

d= modulus of [ax+by+c/root a^2 +b^2]

= modulus of [5+2+(-1)/root (5)^2+(2)^2]

=modulus of [6/root 25+ root 4]

=modulus of [6/root29]

d= 6/root 29