Question

Quick algebra 1 question for 50 points!

Answer 1

If y varies inversely with x then the line must be linear and increasing

And the y intercept must be 0 in y=mx+c

#1

• y=4/3x-2

c=-2

• Not direct

#2

• y=x

Yes

#3

• y=8/x

No

#4

• y=14

Parallel to x axis no direct variation

Answer 2

Answer:

b.  -x + y = 0

Step-by-step explanation:

Direct variation:

Direct variation means "y varies directly as x”:

$y \propto x \implies y=kx$

where k is the (non-zero) constant of variation.

To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.

Equation a

$y=\dfrac{4}{3}x-2$

This is not a direct variation equation as there is an addition of -2.

Equation b

$-x+y=0$

$\implies y=x$

This is a direct variation equation where the constant of variation is 1.

Equation c

$xy=8$

$\implies y=\dfrac{8}{x}$

This is not a direct variation equation as y is inversely proportional to x.

Equation d

$y=14$

This equation does not include the variable x, and so is therefore not a direct variation equation.