Determine whether y varies directly with x and if so, how do you find the constant of variation k for -5y=5x+10.

Solution:

Given the function -5y=5x+10

In order to determine whether y is varying with x or not, we need to transform the given equation into slope-intercept form y=mx+b to identify the slope.

Consider the equation -5y=5x+10

Divide both sides with 5, we get

-y = x + 2

Multiply both sides with a minus, we get

y= -x -2

Here the coefficient of x gives the slope and it is -1.

If y is a positive integer then x becomes a negative integer with the transformation of downshifting by 2 units.

Hence, we can say that y is varying with x with the constant of variation k =-1

How do you determine whether y varies directly with x and if so, how do you find the constant of variation k for -5y=5x+10.

Summary:

Yes, y varies directly and the constant of variation k for -5y=5x+10 is -1.