Determine whether y varies directly with x. If so, find the constant of variation k. 3y=-7x-18
To determine if y varies directly with x, we need to see if the equation can be written in the form y = kx, where k represents the constant of variation.
Let's try to rearrange the given equation in this form:
3y = -7x - 18
Dividing both sides of the equation by 3:
y = (-7/3)x - 6
The equation cannot be written in the form y = kx since the coefficient (-7/3) of x is not a constant. Therefore, y does not vary directly with x in this case.
To determine if y varies directly with x, we need to check if the equation can be written in the form y = kx, where k is the constant of variation.
Given the equation 3y = -7x - 18, let's isolate y on one side of the equation.
Divide both sides of the equation by 3:
(3y) / 3 = (-7x - 18) / 3
Simplify:
y = (-7/3)x - 6
Comparing this equation to the standard form y = kx, we can see that y does not vary directly with x. Therefore, there is no constant of variation (k) in this case.
To determine whether y varies directly with x, we need to rearrange the given equation into the general form for direct variation (y = kx), where k represents the constant of variation.
Starting with the given equation: 3y = -7x - 18
We want to isolate y on one side of the equation, so let's divide both sides by 3:
(3y)/3 = (-7x - 18)/3
This simplifies to: y = (-7/3)x - 18/3
Now we can compare this equation to the general form of direct variation (y = kx):
y = (-7/3)x
From the equation, we can see that y varies directly with x, because it is in the form y = kx. In this case, the constant of variation (k) is (-7/3).