Given the equation $y=\frac{1}{2}x-\frac{4}{3}$, what is the missing variable shown below?
(__, 0)

• A. $\frac{8}{3}$
• B. $\frac{4}{3}$
• C. $2$
• D. $\frac{1}{3}$

Answer: (A)

Verified step by step guidance

1. Identify that the point given is of the form \((__, 0)\), which means the \(y\)-coordinate is 0. We need to find the corresponding \(x\)-value when \(y=0\).
2. Start with the given equation: \(y=\frac{1}{2}x - \frac{4}{3}\).
3. Substitute \(y=0\) into the equation to find \(x\): \(0 = \frac{1}{2}x - \frac{4}{3}\).
4. Add \(\frac{4}{3}\) to both sides to isolate the term with \(x\): \(\frac{4}{3} = \frac{1}{2}x\).
5. Multiply both sides by 2 to solve for \(x\): \(x = 2 \times \frac{4}{3}\).