Math Problem Statement

What is the slope of a line that is perpendicular to a line represented by the equation −3y=8x+6?

Enter your answer, as a fraction in simplest form, in the box.

Solution

To find the slope of a line that is perpendicular to the line represented by the equation 3y=8x+6-3y = 8x + 6, follow these steps:

  1. First, rewrite the equation 3y=8x+6-3y = 8x + 6 in slope-intercept form y=mx+by = mx + b, where mm represents the slope.

    Divide both sides of the equation by 3-3: y=83x+63y = \frac{8}{-3}x + \frac{6}{-3} Simplifying this: y=83x2y = -\frac{8}{3}x - 2 So, the slope m1m_1 of this line is 83-\frac{8}{3}.

  2. The slope of a line perpendicular to this line is the negative reciprocal of m1m_1. The negative reciprocal of 83-\frac{8}{3} is 38\frac{3}{8}.

Thus, the slope of the perpendicular line is 38\frac{3}{8}.

Would you like further explanation on any step?

Here are some follow-up questions:

  1. What is the slope of a line parallel to 3y=8x+6-3y = 8x + 6?
  2. How do you find the equation of a line given its slope and a point?
  3. What is the negative reciprocal of 54\frac{5}{4}?
  4. How do you determine if two lines are perpendicular based on their equations?
  5. What does the slope tell you about the steepness of a line?

Tip: Always remember that perpendicular lines have slopes that multiply to give 1-1.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slopes of Lines

Formulas

Slope-intercept form y = mx + b
Negative reciprocal m_1 * m_2 = -1

Theorems

Perpendicular lines have slopes that are negative reciprocals of each other

Suitable Grade Level

Grades 8-10