the varible X and Y vary directly. write and equation that relates x&y. then find x when y=-4
x=-20/3, Y= -15/8
When two variables vary directly, it means that their values can be related by a linear equation of the form y = kx, where k is a constant. In this case, we need to find the equation relating x and y when they vary directly.
To find the equation, we can use the given values. We have x = -20/3 and y = -15/8. We can substitute these values into the equation y = kx and solve for k.
-15/8 = k * (-20/3)
To solve for k, we need to isolate it. We can do this by multiplying both sides of the equation by -3 and dividing both sides by -20, which is the coefficient of x.
(-3)(-15/8) = k * (-3)(-20/3)
45/8 = k * 20/3
Now, we can simplify the right side by canceling out the common factors of 4:
45/8 = k * 5/3
To isolate k, we can multiply both sides of the equation by the reciprocal of 5/3, which is 3/5:
(3/5)(45/8) = (k * 5/3)(3/5)
(3 * 45)/(5 * 8) = k * 1
135/40 = k
Simplifying the fraction:
27/8 = k
So, the equation that relates x and y when they vary directly is y = (27/8)x.
Now, we can use this equation to find x when y = -4. We substitute y = -4 into the equation and solve for x:
-4 = (27/8)x
To solve for x, we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of 27/8, which is 8/27:
(-4)(8/27) = (27/8)x * (8/27)
-32/27 = x
Therefore, when y = -4 in the equation y = (27/8)x, x is equal to -32/27.