Questions: Find the x-intercept and y-intercept for the following equations. Complete parts (a) through (c) below. a. y=-1/4 x+1 Choose the correct answer below and, if necessary, fill out the answer box to complete your choice. A. The x-intercept is B. There is no x-intercept.

Find the x-intercept and y-intercept for the following equations. Complete parts (a) through (c) below. a. y=-1/4 x+1 Choose the correct answer below and, if necessary, fill out the answer box to complete your choice. A. The x-intercept is B. There is no x-intercept.
Transcript text: Find the $x$-intercept and $y$-intercept for the following equations. Complete parts (a) through (c) below. a. $y=\frac{-1}{4} x+1$ Choose the correct answer below and, if necessary, fill out the answer box to complete your choice. A. The $x$-intercept is $\square$ B. There is no $x$-intercept.
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Solution

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Solution Steps

Step 1: Find the \(x\)-intercept

To find the \(x\)-intercept, set \(y = 0\) in the equation and solve for \(x\).

Given equation: \[ y = \frac{-1}{4}x + 1 \]

Set \(y = 0\): \[ 0 = \frac{-1}{4}x + 1 \]

Step 2: Solve for \(x\)

Rearrange the equation to solve for \(x\): \[ \frac{-1}{4}x = -1 \]

Multiply both sides by \(-4\) to isolate \(x\): \[ x = 4 \]

Step 3: Conclusion

The \(x\)-intercept is \(x = 4\).

Final Answer

The \(x\)-intercept is \( \boxed{4} \).

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