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Direct Variation

by Brooke
(Simpsoville, SC, USA)

Will you explain what direct variation is and give some examples please. This would be greatly appreciated!!



Karin from Algebra Class Says:



Hi Brooke,

Direct variation can be very confusing for many students, so I will explain it the best I can.

We will use the variables x and y. If I say that y varies directly with x, it means that y is directly proportional to x.

y varies directly to x in algebra means y = Kx (where K is any nonzero constant). This is a linear variation.

So if x increases, y is going to increase proportionately.

The following is what I mean by proportionally:
y = Kx
6 = 3(2)
9 = 3(3)
12 = 3(4)

You may have a direct variation such that
y varies directly with the square of x.

That would mean:
y =Kx2 (Where K is any nonzero constant).

12 = 3(2)2
27 = 3(3)2

A problem that you might see in Algebra is:

y varies directly with x. If y is 20 when x is 5, find y when x is 8.

The first sentence tells you the relationship between x and y. "y varies directly with x" so
y = Kx

You know that y = 20 and x =5, so we need to substitute and solve for K which is the constant.

y = Kx
20 = K(5)

20/5 = 5K/5
4 = K

Now we know: y = 4x

So we can substitute 8 for x to answer the question.

y = 4(8)
y = 32.

When x = 8, y = 32.

I hope this helps you to have a better understanding of Direct Variation.

Please let me know if it helped!

Best of luck,
Karin

Comments for Direct Variation

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May 13, 2015
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algebra 1 NEW
by: miranda beasley

If y=3/4 when x=24, find y when x is 12?

Jan 08, 2015
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Question NEW
by: Anonymous

What if X is divided by a number does it still vary directly?

Aug 26, 2014
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nonsense question NEW
by: jheams louie

What if there is radicals in the equation?

Aug 19, 2014
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Variation NEW
by: Anonymous

What is answer when y=30 and x=8

Nov 14, 2012
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answer
by: Anonymous

Use y=kx. First find k. Substitute the y and the x values to find k. 24=k(8). Divide each side by 8. K= 3. We know that k is 3. Use the formula again of y= kx. So it would be y=3(10). Y=30 is your answer.

Apr 09, 2012
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if y varies directlyy with x
by: Anonymous15

If y varies directly with x and y=24 when x=8. What would be the value of y when x=10? Please help me I am majorly confussed.

Dec 13, 2011
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Direct Variation
by: Karin

Shannon,

Are you looking to graph these equations? The best thing to do would be to rewrite the equations in slope intercept form: (y = mx + b) and then graph the equations. You can find great examples for graphing on the following web page:

http://www.algebra-class.com/slope-intercept-form.html

I hope this gets you started!

Karin

Dec 12, 2011
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Direct Variation
by: Shannon

I Need Help With These Problems Ms. Karin :

1. y+8=-x
2. -4=7x+4=3y
3. 0.7x-1.4y=0

Nov 15, 2011
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confused?
by: Anonymous

explain what it means for x and y to vary directly

Nov 08, 2010
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Direct Variation
by: Anonymous

If y varies with x,does x vary with y. If so, what is the relationship between the constants of variation? EXPLAIN

Sep 01, 2010
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pre algrbgra
by: loretta

if y varies directly with x, find the constant of variation if x=8 and y=12
would it be 4?


Karin from Algebra Class Says:



No, 4 would not be the constant of variation.

If y varies directly with x, then we can use the equation:
y = kx where k is the constant of variation.

You know x and y, so we will substitute and solve for k.

x = 8 y = 12

y = kx
12 = k(8)

To solve we will divide both sides by 8.
12/8 = 8k/8

3/2 = k (Simplify 12/8 = 3/2)

Therefore, the constant of variation is 3/2.

Let's check:

y = kx
12 = (3/2)(8)
12 = 12

Yes, it works!

I hope this helps!

Aug 05, 2010
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Direct Variation
by: Karin

Hi,
This is a great question, because most text books and websites only give examples of "positive" direct variation.

Using y = kx, if k is negative (y=-kx) this is still considered direct variation. Except, you are right, as x increases, y decreases; however the two variables are still increasing and decreasing at a constant rate.

A direct variation equation will produce a straight line through the origin (0,0). If k (or the slope) is positive, then the line will rise from left to right, passing through the origin.

If k (or the slope) is negative, then the line will fall from left to right, passing through the origin.

I hope this helps,
Karin

Aug 05, 2010
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variation
by: Anonymous

what if k is negative ?

such as

y = -8x

as the value of x increases, the y does not increased, but decrease...

But we know that the y = kx is direct variation

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