Question


Someone help please thank you show your work 100 points!!

Answer 1

A

Explanation:

y=-2 when x=-4 y=-4 when x=-8

what's given: 4. what's given:2

-4k=-2. -8k=-4

-4/4. -2/4. -8/8. -4/8

k=0.5. k =0.5

0.5(2) =1. 0.5(2)=1

Answer 2

1. (a) no; (b) no; (c) yes
2. y=5x; b=1/2a; m = 5n
3. k = 5; x = 9.8

Explanation:

You want to identify the proportional relations in the given tables and equations, and you want to find and use the constant of variation given that y=35 when x=7.

Proportional relation

A proportional relation is one that has an equation of the form ...

y = kx

One variable is a constant multiple of the other. If the relation cannot be put in this form, it is not a proportional relation.

Application

The value of k in the above equation can be found as ...

k = y/x . . . . . . . divide both sides by x

This is a constant if the relation is proportional.

1a.

y/x = -8/-4 = -4/-2 ≠ 18/6 . . . . . not a proportional relation

1b.

y/x = -4/-5 ≠ 10/2 . . . . . not a proportional relation

1c.

y/x = -12/-3 = 24/6 = 32/8 = 4 . . . . . a proportional relation

2.

You are looking for equations of the form y = kx. The only ones having that form are ...

• y = 5x
• b = 1/2a
• m = 5n

The others represent inverse proportions and a linear (not proportional) relation.

3.

As we saw above, the constant of variation is ...

k = y/x = 35/7

k = 5

Then the value of x can be found from ...

49 = 5x

49/5 = x = 9.8