slope of a line perpendicular to a line with the equation of x= -3/2x +3

The equation you've provided is \( y = -\frac{3}{2}x + 3 \), which is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.

Here, the slope \( m \) of the given line is \( -\frac{3}{2} \).

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

To find the slope of the line perpendicular to the given line, take the negative reciprocal of \( -\frac{3}{2} \):

\[
\text{Perpendicular slope} = -\left(-\frac{2}{3}\right) = \frac{2}{3}
\]

So, the slope of the line perpendicular to the given line is \( \frac{2}{3} \).

Would you like more details on this topic, or do you have any other questions?

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Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What is the relationship between the slopes of parallel lines?
3. How do you find the equation of a line given its slope and a point on the line?
4. What is the significance of the y-intercept in the equation of a line?
5. How do you determine if two lines are perpendicular given their equations?

**Tip:** Remember that the product of the slopes of two perpendicular lines is always \(-1\).

What is the slope of a line perpendicular to a line with the equation y = -3/2x + 3?

Discover how to find the slope of a line perpendicular to the equation y = -3/2x + 3. This guide covers essential algebraic concepts, including slopes of lines and the relationship between perpendicular slopes. Suitable for Grades 8-10.

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