Question

Suppose y varies directly with x and when y=10 when x=-3. What direct variation equation relates x and y? What is the value of y when x =-1?

Answer 1

The direct variation equation is y = (-10/3)x, and when x = -1, the value of y is 10/3.

Step-by-step explanation:

Direct Variation Equation and Calculation of y for a Given x

When we say that y varies directly with x, it means that y = kx, where k is the constant of variation. Given that y = 10 when x = -3, we can find k by substituting these values into the equation: 10 = k(-3) or k = -10/3. Therefore, the direct variation equation that relates x and y is y = (-10/3)x.

To find the value of y when x = -1, we substitute x into our equation: y = (-10/3)(-1) = 10/3. Thus, when x = -1, y is 10/3 or approximately 3.33.

Answer 2

`y=(10)/(3)x`

y = -10/3

Step-by-step explanation:

We have been given that y varies directly with x. Thus, we have the equation

`y=kx`

when y=10 when x=-3

`10=k(3)`

Divide both sides by 3, we get

`k=(10)/(3)`

Thus, the equation which relates x and y is given by

`y=(10)/(3)x`

Now, we have to find the value of y when x = -1

`y=(10)/(3)(-1)\\\\y=-(10)/(3)`