Question

determine the x-intercept of the line whose equation is given:
y = \frac{x}{2} - 3
a. \\ (6, 0)
b. \\ (-6, 0)
c. \\ \left(0, \frac{3}{2}\
ight)
d. \\ \left(-\frac{3}{2}, 0\
ight)
please select the best answer from the choices provided
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Explanation:

Step1: Recall x - intercept definition

The x - intercept of a line is the point where \(y = 0\) on the line. So we need to substitute \(y=0\) into the equation of the line \(y=\frac{x}{2}-3\).

Step2: Substitute \(y = 0\) into the equation

Substitute \(y = 0\) into \(y=\frac{x}{2}-3\), we get the equation \(0=\frac{x}{2}-3\).

Step3: Solve for \(x\)

First, add 3 to both sides of the equation \(0=\frac{x}{2}-3\). We have \(0 + 3=\frac{x}{2}-3+3\), which simplifies to \(3=\frac{x}{2}\). Then, multiply both sides of the equation by 2 to solve for \(x\). So \(x=3\times2 = 6\).
Since the x - intercept occurs at \(y = 0\) and \(x = 6\), the x - intercept is the point \((6,0)\).

Answer:

A. \((6,0)\)