Math Problem Statement

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

Solution

To find the gradient of the line perpendicular to y=3x+5y = 3x + 5, first identify the gradient (slope) of the given line. The slope of the line y=3x+5y = 3x + 5 is 33.

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=13m = -\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!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Geometry

Formulas

m = -1/slope

Theorems

Perpendicular slopes theorem

Suitable Grade Level

Grades 7-9