Questions: Find the x-intercept. y=(8x+16)/(x-4) ([?], 0)

Find the x-intercept. y=(8x+16)/(x-4) ([?], 0)
Transcript text: Find the $x$-intercept. \[ \begin{array}{l} y=\frac{8 x+16}{x-4} \\ ([?], 0) \end{array} \]
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Solution

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Solution Steps

To find the \(x\)-intercept of the function \(y = \frac{8x + 16}{x - 4}\), we need to set \(y = 0\) and solve for \(x\). This involves solving the equation \(8x + 16 = 0\).

Step 1: Set \( y = 0 \) to Find the \( x \)-Intercept

To find the \( x \)-intercept of the function \( y = \frac{8x + 16}{x - 4} \), we set \( y = 0 \). This gives us the equation: \[ 0 = \frac{8x + 16}{x - 4} \]

Step 2: Solve the Equation

Since the fraction is equal to zero, the numerator must be zero. Therefore, we solve: \[ 8x + 16 = 0 \]

Step 3: Simplify and Solve for \( x \)

Subtract 16 from both sides: \[ 8x = -16 \] Divide both sides by 8: \[ x = -2 \]

Final Answer

The \( x \)-intercept is \((-2, 0)\). Therefore, the solution is: \[ \boxed{x = -2} \]

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