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.

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

1. First, rewrite the equation \( -3y = 8x + 6 \) in slope-intercept form \( y = mx + b \), where \( m \) represents the slope.

   Divide both sides of the equation by \( -3 \):
   \[
   y = \frac{8}{-3}x + \frac{6}{-3}
   \]
   Simplifying this:
   \[
   y = -\frac{8}{3}x - 2
   \]
   So, the slope \( m_1 \) of this line is \( -\frac{8}{3} \).

2. The slope of a line perpendicular to this line is the negative reciprocal of \( m_1 \). The negative reciprocal of \( -\frac{8}{3} \) is \( \frac{3}{8} \).

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

Would you like further explanation on any step?

Here are some follow-up questions:

1. What is the slope of a line parallel to \( -3y = 8x + 6 \)?
2. How do you find the equation of a line given its slope and a point?
3. What is the negative reciprocal of \( \frac{5}{4} \)?
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 \( -1 \).

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.

Learn how to find the slope of a line perpendicular to -3y = 8x + 6. This problem focuses on key algebraic concepts such as slopes of lines, negative reciprocals, and slope-intercept form. Suitable for students in Grades 8-10.

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