what does it mean when they say tell wheather the equation represents direct variation. if so then give the constant of variaton

the problem is:
2y-5x=0

y= 5x/2 So as x doubles, so does y. That is a direct variation.

The constant here is 5/2

so it is just the slope of the line??

yes.

alrigth thanks

To determine if an equation represents direct variation, you need to review its form. In general, an equation represents direct variation if it can be written in the form y = kx, where y and x are variables, and k is a constant called the constant of variation.

Now, let's analyze the given equation: 2y - 5x = 0

To determine if it represents direct variation, we need to rearrange the equation into the form y = kx.

Step 1: Move the term 5x to the right-hand side of the equation by adding 5x to both sides:
2y = 5x

Step 2: Divide both sides of the equation by 2 to isolate y:
y = 5/2x

Now, we have the equation in the form y = kx, where k = 5/2. Therefore, the given equation 2y - 5x = 0 represents direct variation, and the constant of variation is 5/2.