Question

What line of perpendicular to the line y = 1/4 x + 3

Answer 1

To find a line perpendicular to the line given by the equation \( y = \frac{1}{4}x + 3 \), you need to determine the slope of the original line and then use the negative reciprocal of that slope for the perpendicular line.

The slope of the line \( y = \frac{1}{4}x + 3 \) is \( \frac{1}{4} \).

The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore:

\[
\text{slope of the perpendicular line} = -\frac{1}{\frac{1}{4}} = -4
\]

Now you have the slope of the perpendicular line, which is \(-4\). If you need to find the equation of the perpendicular line, you will also need a point that this line passes through.

If you have a specific point (let's denote it as \((x_0, y_0)\)), you can use the point-slope form of the line equation, which is:

\[
y - y_0 = m(x - x_0)
\]

where \( m \) is the slope of the line. Substituting in our values:

\[
y - y_0 = -4(x - x_0)
\]

If you don't have a specific point in mind, the perpendicular line can be expressed in slope-intercept form (if you choose an example point). For example, if you choose the point \((0, 0)\):

\[
y - 0 = -4(x - 0)
\]

This simplifies to:

\[
y = -4x
\]

Thus, one example of a line perpendicular to \( y = \frac{1}{4}x + 3 \) is \( y = -4x \). However, many other lines could be perpendicular if they pass through different points.