Answer:
Step-by-step explanation:
Given the following equation:
You can follow these steps in order to solve for "x" and find its value:
1. Apply Distributive property on the right side of the equation:
2. Subract from both sides and add the like terms:
3. Subtract 1.8 from both sides:
4. Finally, divide both side of the equation by -1.5:
y varies directly with x.
The constant of variation is k = 7
Step-by-step explanation:
We have to check whether both vary directly with each other or not.
Every pair of x and y will be considered one by one
If y varies directly with x, it should satisfy y = kx or k = yx
So,
For x= -2, y=-14
For
x=3, y=21
For
x=5, y=35
As k is same for all pairs of x and y, it can be concluded that:
y varies directly with x.
The constant of variation is k = 7
Keywords: Proportion, variation
Learn more about proportion at:
#LearnwithBrainly
If we graph the given points then they appear to be in the shape of cubic function so we can use standard formula of cubic function which is
Plug the given points to get four equations
like first point (3,6) so plug x=3 and y=6 into above equation, we get:
or
6=27a+9b+3c+d
Same way by plugging other points form table, we get total four equations as follows:
6=27a+9b+3c+d, 11=125a+25b+5c+d, 11=64a+16b+4c+d, 21=343a+49b+7c+d
Now we just need to solve these equations for a, b, c and d.
Solving them to get values of a, b, c and d, we get:
Now plug them into
So the required equation will be:
Hence required equation in function notation can be written as
Now to prove that above function is correct, we just graph the given points from table and the obtained function.
After graphing the given points from table and the obtained function, We see that points lie on the graph of
Which proves that our equation is correct.
