Are these two slopes perpendicular?

Question

5x=3y-18
5y=3x+4

Please tell me how you got the answer too. Thanks :-)

Okay so does this mean these slopes are parallel or none?

Answer 1

rearrange the equations to be in the form y = mx + b

So the first one becomes y = (5/3)x + 6
The second one becomes y = (3/5)x + (4/5)

For the slopes to be perpendicular to each other, they need to be negative reciprocals. (look up what this means)

These are not.

Answer 2

ok, so to find slope you need to turn it into slope-line formula
this looks like y=mx+b

m is slope, x and y are variables, and b is slope-intercept

i'll explain it.

first change 5x=3y-18 to slope-line

so you can move the 18 by adding 18 to both sides to get
5x + 18 = 3y, or 3y = 5x + 18
Than you divide by 3 to get y by itself or with a variable of 1, like
(1) y, which is y, cause 1 x y = y
the key to finding point-slope is getting y by itself.
so when you divide by 3, you get
y= 5/3x + 6, because 5 divided by 3 is 5/3, and 18/3 = 6
ok, so y=mx+b is very similar to this.
Since m is slope, that means 5/3 is the slope for this formula

If you do it with the other equation you start off with
5y = 3x + 4
so to get y by itself, you divide both sides by 5
So when you do that you get y = 3/5x + 4/5
So the slope for this line is 3/5.

The slope for both lines compared are 5/3 for the first
and 3/5 for the second.
These slopes are unfortunately not perpendicular, it is close though.
In order to have perpendicular slopes, you have to have
what is called a "negative reciprocal"
That is basically like flipping a fraction and adding a negative.
Here are some examples of negative reciprocals

4/5 => -5/4
2 => -1/2
9/8 => -8/9

see how i flipped the fraction than added a negative sign?

Slopes are ONLY perpendicular when they are negative
reciprocals.

unfortunately for this example, although 3/5 and 5/3 are reciprocals, they are not negatives of each other.

So in conclusion, they are NOT perpendicular.

hope this helps!

P.S. DO NOT LISTEN TO WHAT OTHER PEOPLE SAY
they do not know math obviously

in order to have parallel slopes, they must be EXACTLY THE SAME.
in order to have perpendicular slopes, they have to be NEGATIVE RECIPROCALS
I am a math professor, I hope you take my word over those who
assume they know what they're talking about.

Answer 3

To find the slope of the first equation, you have to move the x term to the right side of the equation and the y term to the left side of the equation, and then divide both sides by -3:

-3y = -5x - 18
y = (5/3)x + 6
so the slope is 5/3 (it's the coefficient of the x term)

To find the slope of the second equation, you need to divide both sides by 5.
y = (3/5)x + 4/5
This gives you a slope of 3/5

Perpendicular lines have slopes that are the negative reciprocals of each other. 5/3 and 3/5 are reciprocals, but since they are both positive, they are not negative reciprocals. Therefore, the lines are not perpendicular. (we generally talk of lines as perpendicular, not slopes)

Answer 4

3y= 5x+18 , y = 5/3x + 6,

slope for this equation is 5/3

5y=3x+4

y = 3/5x + 4/5

slope for second equation is 3/5.

if m1 x m2 = -1, we can say equation 1 and 2 are perpendicular.

where m eans slope.

since 3/5 x 5/3 is not equal to -1, they are nor perpendicular each other.

Answer 5

first, put the equations in y=mx+b format
for the first one that would mean adding -3y to both sides and adding -5x to both sides.
which gives you
-3y=-5x-18
now, because you need the y to be by itself, you divide the whole thing by -3
so that would be in final form
y=5/3x+6
for the other one, you just have to divide by 5 so that the y is by itself.
in final form it is
y=3/5x+4
now to find out if the lines/slopes are perp. you have to look at the slopes for each equation (in this case 5/3 and 3/5) if one of the slopes is the oposite reciprocal of the other, then they are perpandicular, like for the slope say x/y the slope that is perp. to that would be -y/x
both slopes are positive in this case and so neither is the oposite of the other even though they are reciprocals. therefore they are not perp.

Answer 6

No. If you convert both of them to slope-intercept form (y=mx+b) they become:
y=5/3x+6 and
y=3/5x+4/5

Slopes are only perpendicular if when multiplied together, they equal -1 (they are opposite reciprocals).

Answer 7

5x=3y-18, 3y=5x+18, y=5/3x +6. slope is 5/3
5y=3x+4, y=3/5x +4/5. slope is 3/5
the reciprocal of 5/3 is 3/5. so yes, they're perpendicular

Answer 8

No. You got to study more and read books and prove it yourself.