Question

If the value of “y” varies directly with “x” and y = -8 when x = 20, find “y” if x = -4.

Answer 1

To find the value of 'y' when 'x' equals -4, given that y varies directly with x and y = -8 when x = 20, first find the constant of variation (k = -0.4), and then use the direct variation equation (y = -0.4x) to calculate that y = 1.6 when x = -4.

Step-by-step explanation:

When given that y varies directly with x, the relationship between x and y can be represented by the equation y = kx, where k is the constant of variation. To find the value of k, we can use the information that y = -8 when x = 20. Substituting these values into the equation gives us -8 = 20k. Solving for k, we get k = -8/20 = -0.4. Now that we have the constant of variation, we can find y for any value of x using the equation y = -0.4x.

When x = -4, substituting this value into the equation gives us y = -0.4(-4) = 1.6. Therefore, y = 1.6 when x = -4.

Answer 2

y =
`(8)/(5)`

Step-by-step explanation:

Given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 8 when x = 20

k =
`(y)/(x)` =
`(-8)/(20)` = -
`(2)/(5)`

y = -
`(2)/(5)` x ← equation of variation

When x = - 4, then

y = -
`(2)/(5)` × - 4 =
`(8)/(5)`