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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 = -1/3 x.
The point (2, -6) is on the graph of the function.
The equation is y = -3x.
The function is linear.

The equation is y = -3x.

The function is linear.

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

Step-by-step explanation:

The function is linear.

direct variation function is always linear. and linear means a straight line which is true in this case

The equation is y = -3x.

equation of line is y=mx+c

where, m=slope= -3.

it is linear so we are assuming it passes origin, (0,0).

m=(y2-y1)/(x2-x1)

now substituting m=-3 and (0,0) in x1 and y1.

-3=(y2-0)/(x2-0)

-3=y2/x2

y2=-3*x2

where y2=y, x2=x,

therefore,

y=-3x.

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

now,

y=-3x

substituting x=2,

y=-3(2)

y=-6

therefore,

if x=2, y=-6, (2,-6)

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.