Question

Determine whether the equation represents a direct variation. If it does, find the constant of variation:

1. 2y=5x+1
A. Not a direct variation
B. Direct Variation, constant of variation is 5/2
C. Direct Variation, constant of variation is 2/5
D. Direct Variation, constant of variation is 1 -2/5

2. -12x=6y
A. Not a direct variation
B. Direct Variation, constant of variation is ½
C. Direct Variation, constant of variation is 2
D. Direct Variation, constant of variation is -2

3. 0.7x-1.4y=0
A. Not a direct variation
B. Direct Variation, constant of variation is ½
C. Direct Variation, constant of variation is 2
D. Direct Variation, constant of variation is -2​

Answer 1

Answer:

1) A. Not a direct variation 2) D. Direct Variation, constant of variation is -2 C) B. Direct Variation, constant of variation is ½

Step-by-step explanation:

Direct Variation requires that $y=kx$ with k≠0. K its constant of variation and its slope. It is a linear function with b =0

1) Examining 2y =5x + 1. Rewriting it as standard form:

$2y =5x + 1\\\\y=\frac{5}{2}x+\frac{1}{2}$

Since this function cannot be written as y=kx as b ≠ 0 (b=1) then we can say that this is not a direct variation.

A. Not a direct variation

2) $2). -12x=6y \Rightarrow y=-2x$

This linear function has no linear parameter. And its line goes through the origin varying directly. The constant k is equal to -2. So,

D. Direct Variation, constant of variation is -2

3) $0.7x-1.4y=0\\\\-1.4y=-0.7x* (-1)\\y=0.5 \:or\,y=\frac{1}{2}$

The Constant of Variation is 1/2 and K>0. There is a direct variation between x and y of 1/2. So it's B.

B. Direct Variation, constant of variation is ½