Hard to figure out.. Decide whether the pair of lines is parallel, perpendicular, or neither.?

Question

Decide whether the pair of lines is parallel, perpendicular, or neither.
2x + 3y=2
3x + 2y=8

What is the slope of 2x + 3y=2? ____

What is the slope of 3x + 2y=8? _____

The lines are __________

Answer 1

They're neither parallel NOR perpendicular.

They're not parallel (x, y coeffs are not proportional), nor are they parallel (there'd have to be a ' - ' sign on one of the coeffs for that; only then would the products of the slopes be -1, the required value for perpendicularity).

The slope of 2x + 3y = 2 is - 2/3.

The slope of 3x + 2y = 8 is - 3/2.

(The slope is ' m ' where the eqn. is written as y = m x + b.)

And, as already stated, they are NEITHER parallel nor perpendicular. ###

Live long and prosper.

### Note that you really DON'T have to go through the tedious step of actually EVALUATING what each separate slope is, to reach this conclusion. I already gave all the necessary reasoning in the two parentheses included in my second sentence, above. It is flogging a pedantic dead horse to subject you to this tedium.

Answer 2

No problem:

To find the line's slope easiest, put it in slope-intercept form.
To do that, just solve for y, like this:

2x + 3y = 2
... - 2x from both sides...
3y = -2x + 2
...and divide by 3 to get y by itself...
y = -2/3 x + 2/3
...so on this one, the slope is -2/3 and the y-intercept is 2/3.

Then you do it for the second one, too. Since you need the practice ('cause I'm not going to just do your work for you), I let you do that one.

Now, the answer to the question will all be in the slopes:
-- If the slopes of the two lines are = then the lines are parallel (unless the y-intercepts are also =, but that won't happen unless they're really both the same line).
-- If the slopes are opposite reciprocals of each other, then that means the lines are perpendicular. In this case, perpendicular to a slope of -2/3 would be 3/2 (which is the same as 1&1/2).

...And if the slopes aren't the same (=), and the slopes aren't opposite-reciprocals, then the lines are "neither"!

And now you're all set to do your problem!

(at least, the parts I haven't done for you already... :)

Barjesse37

Answer 3

The lines are parallel if the slopes turn out to be the same. They are perpendicular if the slopes are negative reciprocals of each other.
First, get the lines into the form y = mx + b (where m is the slope and b is the y intercept), by solving each equation for y.

2x + 3y = 2
3y = -2x + 2(subtracted 2x from both sides)
y = (-2/3)x + 2 (divided both sides by 3.)

Compare this to y = mx + b...
The slope is -2/3

Now for the other line...
3x + 2y = 8
2y = -3x + 8 (subtracted 3x from both sides.)
y = (-3/2)x + 4 (divided both sides by 2.)
Compare this to y = mx + b...
The slope of this line is -3/2
Now compare the two slopes.
As you can see, -3/2 and -2/3 are reciprocals of each other, BUT they aren't negative reciprocals. So the lines are not perpendicular. But they aren't the same slope either, so they aren't parallel. Therefore, they're neither.

Answer 4

First put in slope intercept form 4x+3y=6 3x - 4y = 8 3y = -4x + 6 Divide by 3 y = -4/3x + 2 -4y = -3x + 8 divide by -4 y = 3/4x - 2 My slope is -4/3 and 3/4 so it is opposite reciprocal so they are perpendicular, to be parallel it would have to be the same slope. Good Luck!

Answer 5

Put the equations into standard form: y = mx + b

'm' is the slope of the line.

If parallel, 'm' will be the same for both lines.
If perpendicular, the 'm' of one line will be the negative reciprocal of the other ie -1/m.

If they are neither the same nor negative reciprocals of each other, then they are neither parallel nor perpendicular.

By inspection: m1 = -2/3, m2 = -3/2

The lines are neither parallel nor perpendicular.

Answer 6

You should shuffle each equation around to slope intercept form y = Mx + B. M is the slope

The lines will be parallel if M is equal for both
The lines will be perpendicular if M of the first line is -1/M of the second.
The lines will otherwise eventually intercept somewhere.
RSaunders quick peek looks correct.

Answer 7

By inspection, the slopes are different but not reciprocal, so the lines will intersect but are not perpendicular. You can figure out the slopes with simple arithmetic.

Answer 8

1st slope is -2/3. 2nd slope is -3/2. Lines are perpendicular.

Answer 9

3y = - 2x + 2
y = (- 2/3).x + 2 / 3------->m1 = (- 2/3)

2y = - 3x + 8
y = (-3/2).x + 4--------->m2 = (-3/2)
m1 x m2 = (-2/3) x (-3/2) = 1

Answer is NEITHER