Question

2y=5x+1

Not a direct variation
Direct variation, constant of variation is -
Direct variation, constant of variation is
Direct variation, constant of variation is 1--

Answer 1

Explanation:

he whole assignment seems to deal only with one simple concept, a direct variation

Sometimes text or your notes have definitions that are difficult to understand.

Here is the definition that is easy to understand:

A direct variation gives you an equation that contains no constants, and there are no exponents on the two variables.

e.g. y = 8x is a direct variation,

but y = 8x + 4 is NOT, since I see a constant of 4

a direct variation can be written in the form

y = kx , where k is the constant of variation

#1, not a variation, I see a +1 sitting there as a constant

#2, yes it is a direct variation:

-12x = 6y

6y = -12x

y = -2x

so the constant of variation is -2 , if y varies directly with x

or

-12x = 6y

x = -(1/2)x

now the constant of variation is -1/2 , if x varies directly as y

so it depends how you express the equation, either in terms of x or in terms of y

#3,

.7x - 1.4y = 0

.7x = 1.4y

1.4y = .7x

y = (.7/1.4)x = (1/2)x

so , yes it is, and the constant of variation is 1/2

From #4 on, you have to first find the equation.

I will do #4, you try the remaining.

#4, they tell us it is a direct variation, so it must look like

y = kx

They give us x=2 when y = -10

let's plug in those values:

-10 = k(2)

2k = -10

k = -5

aaahhhh, so y = -5x is our equation

#6, same way, just some fractions to deal with

#7, to graph, pick any x, and find the y to get ordered pairs,

e.g. let x = 3, then y = (1/3)(3) = 1, --> point(3,1)

let x = 9, then y = (1/3)(9) = 3 ---> point (9,3)

plot those two points, and join with a straight line

Notice how I picked multiple of 3's for my x's so I could take 1/3 of the x without ending up with fractions?

#8 , same as #7, pick multiples of 2 for your x's

#9 and #10 are the same type

#9

assume it is a direct variation, then its equation must be

y = kx

use the first given data: x = 3, y = 5.4

then 5.4 = k(3)

3k = 4.5

k = 1.5

equation is y = 1.5x

do the other points satisfy our equation?

for (7, 12.6)

is 12.6 = 1.5(7) ?

12.6 = 10.5 ??? NO, so the given data is NOT a direct variation

#10 same way

Answer 2

Answer:1. 2y=5x+1 answer is A Not a direct variation

2. -12x=6y answer is D Direct variation, constant of variation is -2

3. 0.7x-1.4y=0 answer is B Direct variation, constant is 1/2

4. y=-10 when x=2 answer is A y=-5x

5. y=7 1/2 when x=3 answer is C y=5/2 x

6. y=10.4 when x=4 answer is D y=2.6x

7. y=1/3 x answer is A the graph that reads (6, 2) where the green arrow is on the top right portion and on the bottom left is (-6, -2)

8 y=-1/2 x answer is C graph

9. the table x is first 3, 7, 12 y is next 5.4, 12.6, 21.6 answer is B Direct variation, y=1.8x

10. the table x is first -2, 3, 8 y is next 1, 6, 11 answer is A not a direct variation

p.s. this is for the direct variation practice

hope i helped

Explanation: