A line is perpendicular to y = -x-9
What is the slope of this
perpendicular line?
A. -1/4
B. 1/4
a-4
D. 4

Note: your answer options suggest as if your actual question was

y = -4x - 9 instead of y = -x-9

But, anyways I am solving with respect to both equations

Please check the explanation.

Step-by-step explanation:

IN CASE YOUR EQUATION ⇒ y = -x - 9

The slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the line

comparing with the slope-intercept form (y = mx+b) of the line

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -1

perpendicular slope = – 1/m = -1/-1 = 1

Thus the slope of this  perpendicular line will be:  1

IN CASE YOUR EQUATION ⇒ y = -4x - 9

Given the line

comparing with the slope-intercept form (y = mx+b) of the line

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -4

perpendicular slope = – 1/4 = -1/-4 = 4

Thus the slope of this  perpendicular line will be: 4

Hi there!

Using the triangle exterior angle theorem, we know that:

∠4 = the other two angles of the triangle combined (both are given)

Thus:

∠4 = 51 + 51 = 102°