y is partly constant and partly varies as x, when x=5,y=8 and when x=6,y=4.find the equation of the variation of x and y.find y when x=15
I don't know please just help me by working it out.Thanks.
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it is very cunny ,I worked many times till I did not get it.
I have get the answer
I don't fear it
To find the equation of the variation between x and y, we need to determine the relationship between them. From the given information, we know that y is partly constant and partly varies with x.
When x = 5, y = 8.
When x = 6, y = 4.
Let's analyze the change in y as x increases from 5 to 6. We can observe that y decreases by 4 units when x increases by 1 unit. This suggests that the variable part of y varies at a constant rate of -4 units per 1 unit change in x.
To find the constant part of y, we can substitute the values of x and y from either point (5, 8) or (6, 4) into the equation y = k + mx, where k represents the constant part, and m represents the variable part.
Using the point (5, 8) in the equation, we have:
8 = k + 5m
Now, we can substitute the point (6, 4) into the equation to find m:
4 = k + 6m
We can solve these two equations simultaneously to find the values of k and m.
8 = k + 5m ...(1)
4 = k + 6m ...(2)
By subtracting equation (2) from equation (1), we can eliminate k:
8 - 4 = (k + 5m) - (k + 6m)
4 = -m
m = -4
Substituting the value of m into equation (1):
8 = k + 5(-4)
8 = k - 20
k = 28
Now we have the values of k = 28 and m = -4. Hence, the equation relating x and y is y = 28 - 4x.
To find y when x = 15, we can substitute the value of x into the equation:
y = 28 - 4(15)
y = 28 - 60
y = -32
Therefore, when x = 15, y = -32.
y = kx + c
You have the points (5,8) and (6,4) so
5k+c = 8
6k+c = 4
Now just solve for c and k, and find y as desired.