What is the gradient of the line perpendicular to y=3x+5

To find the gradient of the line perpendicular to \( y = 3x + 5 \), first identify the gradient (slope) of the given line. The slope of the line \( y = 3x + 5 \) is \( 3 \).

The gradient of a line that is perpendicular to another is the negative reciprocal of the original line's slope. Therefore, the gradient of the perpendicular line is:

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

If you have any questions or would like further details, let me know! Here are some related questions you might find interesting:

1. How do you determine the slope of a line from its equation?
2. What is the general equation of a line given its slope and a point?
3. Can you explain how to graph a line given its slope?
4. How do you find the equation of a line perpendicular to a given line through a specific point?
5. What other properties are important when working with parallel and perpendicular lines?

**Tip:** Always remember that perpendicular slopes are negative reciprocals of each other!

What is the gradient of the line perpendicular to y=3x+5?

Discover how to find the gradient of the line perpendicular to y=3x+5. This problem illustrates key concepts in algebra and geometry, focusing on slopes and their relationships. Suitable for students in Grades 7-9.

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