Can someone help me with Direct Variation?

[Suthern_bell]

I have been given 55 problems such as this, plus I have a test over it Thursday, I am in desperate need of help.

y= -6/7 when x= -18/35

y=2 when x=1

I have no idea how to solve these! Thanks in advance for the help.

 

[wjm11]

Direct Variation:

y= -6/7 when x= -18/35

This is very easy, IF you know what direct variation means. (Suggest you read your book!). Simply, it means that y increases as x increases, but more specifically (and graphically), it’s a line that passes through the origin and has a positive slope.

Knowing that the line passes through the origin is key, because that means you always know one of the points on the line: (0,0). When they give you another piece of info, such as y= -6/7 when x= -18/35, they’re giving you a second point (-18/35,-6/7), and it’s suddenly very easy to write the equation for the line. To find the slope, simply use the slope formula:

m = (y1-y2/x1-x2)

However, notice that since one of the points is (0,0), you can simplify this to

m = (y1-0/x1-0) = (y1/x1)

In this case that would be

m = ((-6/7)/(-18/35)) = (6/7)*(35/18) = 5/3

Therefore, the equation of the direct variation line would be y = (5/3)*x.

 

[Denis]

You can also look at direct variation this "easy" way:

a = 12 when b = 9 ; what is a if b = 15?
solution: 12 / 9 * 15 = 20

what is b if a = 18?
solution: 9 / 12 * 18 = 13.5

It's really as easy as:
if 5 apples cost $1.25, how much does 7 apples cost?
solution: 1.25 / 5 * 7 = 1.75
Notice that 1.25 / 5 = .25, which is the price of 1 apple;
then that's multiplied by 7; capish?

Do a http://www.google.com search on "direct variation";
you'll find lots of sites that'll make it easy for you...