A straight line passes through A (-2, 0) and B (2,-k). The line is perpendicular to a line 34+2x=5 Determine the value of K.

Step-by-step explanation:

Let the slope of the first line be m1

Let the slope of the second line be m2

If both lines are perpendicular, then;

m1m2 = -1

Get m1, the slope of the line passing through A (-2, 0) and B (2,-k).

m1 = y2-y1/x2-x1

m1 = -k-0/2-(-2)

m1 = -k/4

Get the slope of the line 3y + 2x = 5

Rewrite the equation;

3y = -2x + 5

y = -2/3 x + 5/3

Hence the slope of the line m2 is -2/3

Since m1m2 = -1, then;

-k/4(-2/3) = -1

2k/12 = -1

k/6 = -1

k = -6

Hence the value of k is -6

the circle one