Question

For each function, y varies directly with x. Find each constant variation. Then find the value of y when x= -0.3

1. y=2 when x= -1/2

2. y= 2/3 when x= 0.2

3. y=7 when x= 2

4. y=4 when x= -3

Answer 1

can someone at least explain it to me or show me an example? :c

Answer 2

"y varies directly with x" means y = constant * x or
y = kx ----- (1)
1. when x = -1/2, y = 2
Put it in (1):
2 = k * (-1/2)
multiply by 2:
4 = k * (-1)
4 = -k
k = -4
y = -4x

"find the value of y when x= -0.3"
y = -4x = (-4) * (-0.3) = 1.2

Answer 3

So for each problem, start with y = kx
They give you one x and one y value.
Put it in y = kx and find k.
Then put x = -0.3 and find y.

Answer 4

Why would i multiply it though; for the first one?;o

Answer 5

The easiest way to do these type of problems is to set it up like a proportion

Answer 6

We are trying to solve for k.
2 = k * (-1/2)
To solve for k, we need to isolate k.
On the right hand side, there is a 2 in the denominator.
If we multiply both sides by 2, we can get rid of the 2 in the denominator:
2 * 2 = k * (-1/2) * 2
4 = k * (-1)
4 = -k
multiply both sides by -1:
-4 = k or
k = -4

So y = -4x

Answer 7

@megan_tanuis The problem states: "Find each constant variation. Then find the value of y when x= -0.3" So we have to find k in each case.

Answer 8

But its telling you to find y. if you set it up like \[\frac{ x }{ y }\times \frac{ x }{ y }\] then cross multiply, you can get the answer that way too

Answer 9

Unless I'm taking this the wrong way and you arent supposed to use the first set of numbers given with the others in 1-5

Answer 10

Then yes, you're right if thats the case.

Answer 11

Each problem has its own constant of variation.
They want the "constant of variation" for each problem.
Then they want the y value when x = -0.3 for each problem.

Answer 12

@aum okay so for #2

\[y=\frac{ 2 }{ 3 }, x=0.3\]
y=kx

\[\frac{ 2 }{ 3}=k \times 0.3\]

multiply both sides by 3?
and i'll get
\[3\times \frac{ 2 }{ 3 }=k \times0.3\times3\]
\[9=k\times0.9\]?

Answer 13

3 x 2/3 = 2 (not 9)

Answer 14

oh okay..

so i'll end up having..
\[2=k\times0.9\]
and multiply each side by 2?

Answer 15

We want to isolate k. So we got to get rid of the 0.9. Divide both sides by 0.9
2/0.9 = k
Normally it is not a good practice to have both decimal and fraction together. So get rid of the decimal by multiplying top and bottom by 10:
k = 2 / 0.9 = 2*10 / (0.9 * 10) = 20/9

Answer 16

So for problem #2, the constant of variation is 20/9

y = kx
y = 20/9 * x
Find y when x = -0.3
y = 20/9 * (-0.3) = -6/9 = -2/3

Answer 17

so \[y=-\frac{ 2 }{ 3 }\] ?

Answer 18

I just noticed you made a mistake in copying the problem about 6 replies before this. Problem #2 is: y= 2/3 when x= 0.2 (you had it as 0.3)
y = kx
2/3 = k * 0.2
multiply by 3:
2 = 0.6 * k
divide by 0.6
2/0.6 = k
multiply top and bottom of fraction by 10 to get rid of the decimal:
20/6 = k
simplify fraction:
10/3 = k or
k = 10/3 is the constant of variation.

"find the value of y when x= -0.3"
y = kx
y = 10/3 * x
x = -0.3
y = 10/3 * (-0.3) = 10 * (-0.1) = -1

Answer 19

3. y=7 when x= 2
y = kx
7 = k * 2
divide by 2:
7/2 = k or
k = 3.5 is the constant of variation
y = 3.5x

"find the value of y when x= -0.3"
y = 3.5 * (-0.3) = -1.05

You can finish the fourth problem the same way.