How do I find the Rate of Change for an equation

How do I find the rate of change for this equation?
5x+3y=-2
Please explain how to get the answer.

The first step is to the equation in y = form. Solve for y.

5x + 3y = -2
3y = -5x - 2
y = -(5/3)x - 2/3

The rate of change will always be the number infront of the x value. Therefore in this case the rate of change would be -5/3.

Assuming you are reffering to the rate of change of y with respect to x, this is you you find it.

Solve for y in terms of x. First subtract 5x from each side to give:

3y = - 5x -2

Now, divide each side by 3 to give:

y = (-5/3)x - 2/3

That is a line with slope -5/3. The slope by definition is the rate of change so your answer is -5/3.

If you know calculus you could take the derivative of y with respect to x and get the same answer, but in this case just identifying the slope is enough.

To find the rate of change of an equation you have to take the derivative of it.

To start, solve for y.

y= (5x+2) / -3

so dy/dx= -5/3.

Therefore the graph will have a rate of change of -5 / 3.

Note that the rate of change is equal to the slope of the graph y= (5x+2) / -3.

You don't find rate of change for an equation, but for one variable with respect to another variable

5x + 3y = −2
5 dx + 3 dy = 0
3 dy = −5 dx
dy/dx = −5/3
dx/dy = −3/5

So rate of change of y with respect to x = dy/dx = −5/3
and rate of change of x with respect to y = dx/dy = −3/5

Implicit differetiation.
diff. 5x = 5
diff. 3y = 3 dy/dx (product rule)
diff -2 = 0

so we have 5 + 3 dy/dx = 0 so dy/dx = -5/3

You could get the same answer by making y the subject then differentiating as normal.

3y = - 2 - 5x
y = (-2/3) - (5/3) x
dy/dx = - 5/3