Question

Calculate an equation for a line that is perpendicular to the graphed line.
y=−23x+4
y=32x+6
y=23x+6
y=32x+4

Answer 1

To find an equation for a line that is perpendicular to another line, we need to know the slope of the original line. The slope-intercept form of a linear equation is generally given as \( y = mx + b \), where \( m \) is the slope.

The given line has the equation \( y = -23x + 4 \). Here, the slope \( m \) is \(-23\).

For two lines to be perpendicular, the product of their slopes must equal \(-1\). Therefore, if one line has a slope of \( m_1 \), the slope \( m_2 \) of a line that is perpendicular to it can be found using the formula:

\[
m_1 \cdot m_2 = -1
\]

In our case:

\[
-23 \cdot m_2 = -1
\]

To solve for \( m_2 \):

\[
m_2 = \frac{-1}{-23} = \frac{1}{23}
\]

Now we have the slope of the line that is perpendicular to the original line, which is \( \frac{1}{23} \).

Next, we can write the equation of the new line. Since the equation of a line can also be written in the slope-intercept form as \( y = mx + b \), we will require a point through which this line will pass. If no specific point is given, we can use the y-intercept as zero or any point.

For simplicity, let’s assume the new line goes through the origin (0, 0). Thus:

\[
y = \frac{1}{23}x + 0
\]

This equation simplifies to:

\[
y = \frac{1}{23}x
\]

If you want a different y-intercept, you can adjust \( b \) accordingly but the slope will remain the same.

So, the equation of a line that is perpendicular to \( y = -23x + 4 \) is:

\[
y = \frac{1}{23}x
\]

If you have a specific point or requirement, you can provide that for a more tailored answer.