Answer:
The point [tex](2, -6)[/tex] is on the graph of the function.
The equation is [tex]y=-3x[/tex]
The function is linear.
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
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
[tex]k=-3[/tex]
the equation is equal to
[tex]y=-3x[/tex]
therefore
statements
case A) The equation of the function is y = -x
The statement is false
case B) The point [tex](2, -6)[/tex] 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
[tex]-6=-3(2)[/tex]
[tex]-6=-6[/tex] ------> is true
case C) The equation is [tex]y=-3x[/tex]
The statement is true
case D) The function is linear.
The statement is true
The equation represent a linear direct variation
