Thread: XY variables vary directly........

1. XY variables vary directly........

once... again... worksheet. The variables x y vary directly. Use the given values to write an equation that relates x and y

x=8 , y =24

x=3 , y=36

I have no idea... how to do this

2. Originally Posted by n_duncan2010
once... again... worksheet. The variables x y vary directly. Use the given values to write an equation that relates x and y

x=8 , y =24

x=3 , y=36

I have no idea... how to do this
if x and y vary directly, it means that one is a constant times the other, that is:

x = ky

for the first:
x = 8, y = 24
=> 8 = 24k
=> k = 1/3
so x = (1/3)y
or better yet:
y = 3x

for the second:
x = 3, y = 36
=> 3 = 36k
=> k = 1/12
so x = (1/12)y
or y = 12x

3. I interpret the question to mean derive the equation of the line with those two points:

y = mx +c

m is the gradient = (y1-y2)/(x1-x2) = (24-36)/(8-3) = -2.4

y = -2.4x + c

Substitute in one of the (x,y) pairs to find c:

24 = -2.4(8) + c => c = 24 + 19.2 = 43.2

y = 43.2 - 2.4x

4. Originally Posted by jl5000
I interpret the question to mean derive the equation of the line with those two points:

y = mx +c

m is the gradient = (y1-y2)/(x1-x2) = (24-36)/(8-3) = -2.4

y = -2.4x + c

Substitute in one of the (x,y) pairs to find c:

24 = -2.4(8) + c => c = 24 + 19.2 = 43.2

y = 43.2 - 2.4x
well, your way seems to make sense, but i believe it was two different questions for the following reason:

By definition, we say x and y vary directly if:
x = ky

I have never seen a definition of direct variation, or varying directly that accounts for the possibility of a lone constant. that is,

x = ky + c is not direct variation by definition

and so i assumed it was two separate problems. plus, n_duncan2010 never said anything about me putting down two answers, so i guess it was really two problems

5. I would assume that same as you, Jhevon, but n_duncan2010 didn't give very clear instructions.