What is the slope x 4y equals 12?

Answer 1

I presume that since you labeled this as a Calculus problem that you mean x * 4y = 12?

x * 4y = 12 --->

4y = 12 / x --->

y = 3 / x --->

y = 3 * x^(-1)

You will notice that this function is not a line, but a curve. The slope will be different at different points on the line. Thus, we can't find the slope of the entire function, but we CAN find a function which gives us the slope of a tangent line at any point on the function. We do this by taking the derivative.

For f(x) = a * x^(n)

f'(x) = a * n * x^(n-1)

Using a = 3 and n = -1, we have:

y = f(x) = 3 * x^(-1)

dy/dx = f'(x) = 3 * -1 * x^(-1 - 1) = -3 * x^(-2)

So your answer will be:

dy/dx = -3 * x^(-2)