Given the equation $y=\frac{1}{2}x-\frac{4}{3}$, what is the missing variable shown below?


(__, $\frac{20}{3}$)

• A. $8$
• B. $12$
• C. $24$
• D. $16$

Answer: (D)

Verified step by step guidance

1. Identify the given equation: \(y = \frac{1}{2}x - \frac{4}{3}\).
2. Recognize that the point is given as \((\_, \frac{20}{3})\), where the \(y\)-value is \(\frac{20}{3}\) and the \(x\)-value is unknown.
3. Substitute \(y = \frac{20}{3}\) into the equation: \(\frac{20}{3} = \frac{1}{2}x - \frac{4}{3}\).
4. Add \(\frac{4}{3}\) to both sides to isolate the term with \(x\): \(\frac{20}{3} + \frac{4}{3} = \frac{1}{2}x\).
5. Combine the fractions on the left side and then multiply both sides by 2 to solve for \(x\): \(x = 2 \times \left( \frac{20}{3} + \frac{4}{3} \right)\).