given y = 2/3x - 6, write a possible equation for a line that is perpendicular to this line

To find a line that is perpendicular to the given line \( y = \frac{2}{3}x - 6 \), we need to use the concept that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the given line is \( \frac{2}{3} \). The negative reciprocal of this slope is:

\[
-\frac{1}{\frac{2}{3}} = -\frac{3}{2}
\]

Thus, the slope of the perpendicular line must be \( -\frac{3}{2} \).

A possible equation for a line perpendicular to the given line can be written as:

\[
y = -\frac{3}{2}x + b
\]

Here, \( b \) is the y-intercept, and you can choose any value for \( b \). For example, let's take \( b = 4 \). The equation would then be:

\[
y = -\frac{3}{2}x + 4
\]

This is a possible equation for a line that is perpendicular to the given line.

Would you like more details or have any questions? Here are some related questions:

1. How do you find the slope of a line given its equation?
2. What is the general form of a linear equation?
3. How do you determine the negative reciprocal of a slope?
4. Can you graph lines that are perpendicular to each other?
5. How can we find the point of intersection between two perpendicular lines?

**Tip:** Perpendicular slopes are negative reciprocals; multiplying them together always results in -1.

Learn how to find the equation of a line perpendicular to y = 2/3x - 6. This problem covers key algebraic concepts like finding slopes, understanding negative reciprocals, and writing linear equations. Suitable for students in Grades 8-10.

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