Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

Verified step by step guidance

1. Understand the concept of direct variation: If y varies directly as x, it means y = kx, where k is the constant of proportionality.
2. Use the given values y = 20 when x = 4 to find the constant k by substituting into the equation y = kx, which gives 20 = k \times 4.
3. Solve for k by dividing both sides of the equation by 4, resulting in k = \frac{20}{4}.
4. Write the direct variation equation with the found constant k: y = kx.
5. Substitute x = -6 into the equation y = kx to find the corresponding value of y.

Key Concepts

Direct Variation

Direct variation describes a relationship where one variable is a constant multiple of another, expressed as y = kx. If y varies directly as x, increasing x results in a proportional increase or decrease in y, depending on the constant k.

Constant of Variation

The constant of variation (k) is the fixed ratio between y and x in a direct variation equation. It can be found by dividing y by x using known values, allowing you to write the specific equation for the relationship.

Solving for Unknown Values

Once the constant of variation is known, substitute the given x value into the equation y = kx to find the corresponding y. This process involves simple substitution and multiplication to solve for the unknown variable.