Consider the line 9x-6y=-3 .

What is the slope of a line parallel to this line?

What is the slope of a line perpendicular to this line?

Well, if you're looking for a serious answer, let me break it down for you. The given equation is in the form of y = mx + b, where m is the slope of the line. So, 9x - 6y = -3 can be rearranged as -6y = -9x - 3, and dividing everything by -6, we get y = 3/2x + 1/2.

Now, the slope of a line parallel to this one would be the same since parallel lines have the same slope. Therefore, the slope of a line parallel to this line is 3/2.

As for the slope of a line perpendicular to this line, we need to find the negative reciprocal of the slope. In this case, the negative reciprocal of 3/2 is -2/3. So, the slope of a line perpendicular to this line is -2/3.

I hope that answers your question! If you want a funny answer, I could tell you that the slope of a line parallel to this line is as steep as an elephant climbing a tree, and the slope of a line perpendicular to this line is as slippery as a banana peel on an ice rink. But that would just be clowning around!

To determine the slope of a line parallel to the given line, we need to observe that parallel lines have the same slope.

Step 1: Convert the given line to slope-intercept form (y = mx + b).
Starting with 9x - 6y = -3:
-6y = -9x - 3 (subtract 9x from both sides)
y = (3/2)x + 1/2 (divide both sides by -6)

The slope-intercept form of the given line is y = (3/2)x + 1/2.
Thus, the slope of this line is 3/2.

Therefore, any line parallel to this line will have the same slope of 3/2.

To determine the slope of a line perpendicular to the given line, we need to recognize that perpendicular lines have slopes that are negative reciprocals of each other.

Step 2: Find the negative reciprocal of the slope of the given line.
The slope of the given line is 3/2.
The negative reciprocal of 3/2 is -2/3.

Therefore, any line perpendicular to this line will have a slope of -2/3.

the perpendicular line is -2

the parallel line is 3/2

so is the perpendicular line is -2/3?

What is the parallel line?

First you have to put your line into

y = mx + b format.

9x - 6y = -3

-6y = -9x -3
y = 9/6 x - 3
y = 3/2 x - 3

Parallel lines have the same slope.
m represents you slope.

Perpendicular lines have slopes that are negative reciprocals of each. flip the fraction and include the opposite sign. In this case it would be -2/3

Also, if you multiple the slopes of two perpendicular lines you will always get -1 as an answer.