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 that y is equal to a constant k multiplied by x. This can be written as the equation \(y = k \times x\).
2. Use the given values to find the constant of variation k. Substitute \(y = 20\) and \(x = 4\) into the equation \(y = kx\) to get \$20 = k \times 4$.
3. Solve for k by dividing both sides of the equation by 4: \(k = \frac{20}{4}\).
4. Now that you have the value of k, use it to find y when \(x = -6\). Substitute \(k\) and \(x = -6\) into the equation \(y = kx\) to get \(y = k \times (-6)\).
5. Simplify the expression to find the value of y when \(x = -6\).

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 multiplier in a direct variation equation y = kx. It can be found by substituting known values of x and y into the equation, allowing you to determine k and use it to find unknown values.

Solving for Unknowns in Variation Problems

Once the constant of variation is known, you can solve for unknown variables by substituting given values into the direct variation formula. This process involves algebraic manipulation to find the missing value, such as y when x is given.