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--

Step-by-step 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

aaa, 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

ok

step-by-step explanation:

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.