Question

Which line is perpendicular to the line y=1/4x+3
?

Option #1: y=1/4x+5


Option #2: y=4x+5


Option #3: y=−4x+5


Option #4: y=−1/4x+5

(1 point)
The line in Option #
is perpendicular to the line y=1/4x+3
.

Answer 1

To determine which line is perpendicular to the line \( y = \frac{1}{4}x + 3 \), we need to understand that two lines are perpendicular if the product of their slopes is \(-1\).

The slope of the given line \( y = \frac{1}{4}x + 3 \) is \( \frac{1}{4} \). Therefore, the slope of any line that is perpendicular to it must be the negative reciprocal of \( \frac{1}{4} \):

\[
m = -\frac{1}{\left(\frac{1}{4}\right)} = -4
\]

Now, let's check each option to find the line with a slope of \(-4\):

1. **Option #1:** \( y = \frac{1}{4}x + 5 \) → Slope = \( \frac{1}{4} \)
2. **Option #2:** \( y = 4x + 5 \) → Slope = \( 4 \)
3. **Option #3:** \( y = -4x + 5 \) → Slope = \( -4 \)
4. **Option #4:** \( y = -\frac{1}{4}x + 5 \) → Slope = \( -\frac{1}{4} \)

The correct option that has a slope of \(-4\) is **Option #3: \( y = -4x + 5 \)**.

Thus, the line in Option **3** is perpendicular to the line \( y=\frac{1}{4}x+3 \).