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 \((x, 0)\), meaning the \(y\)-coordinate is zero. We need to find the \(x\)-value when \(y = 0\).
2. Start with the equation \(y = \frac{1}{2}x - \frac{4}{3}\) and substitute \(y = 0\) to find \(x\): \(0 = \frac{1}{2}x - \frac{4}{3}\).
3. Add \(\frac{4}{3}\) to both sides to isolate the term with \(x\): \(\frac{4}{3} = \frac{1}{2}x\).
4. To solve for \(x\), multiply both sides of the equation by the reciprocal of \(\frac{1}{2}\), which is \$2$: \(x = 2 \times \frac{4}{3}\).
5. Simplify the right side by multiplying the numerators and denominators: \(x = \frac{8}{3}\). This gives the missing \(x\)-value for the point \((\frac{8}{3}, 0)\).