Question

Select all that apply. The slope of the graph of a direct variation function is -3. Which of the following is true? The equation of the function is y = -x. The point (2, -6) is on the graph of the function. The equation is y = -3x. The function is linear.

Answer 1

B c and d

Explanation:

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Answer 2

The point
`(2, -6)` is on the graph of the function.

The equation is
`y=-3x`

The function is linear.

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so in this problem

we have

`k=-3`

the equation is equal to

`y=-3x`

therefore

statements

case A) The equation of the function is y = -x

The statement is false

case B) The point
`(2, -6)` is on the graph of the function.

The statement is true

Because , the ordered pair satisfy the equation

so

For x=2, y=-6

substitute

`-6=-3(2)`

`-6=-6` ------> is true

case C) The equation is
`y=-3x`

The statement is true

case D) The function is linear.

The statement is true

The equation represent a linear direct variation