What is the rate of change of the function y, equals, x, plus, 2y=x+2
To find the rate of change of a function, we need to determine the derivative of the function.
First, let's rewrite the equation in slope-intercept form:
2y = x + 2- y
3y = x + 2
y = (1/3)x + 2/3
Now, we can differentiate both sides of the equation with respect to x:
dy/dx = d/dx [(1/3)x + 2/3]
dy/dx = (1/3)(d/dx)(x) + d/dx(2/3)
dy/dx = (1/3)(1) + 0
dy/dx = 1/3
Therefore, the rate of change of the function y = x + 2y = x + 2 is 1/3.