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 , follow these steps:
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First, rewrite the equation in slope-intercept form , where represents the slope.
Divide both sides of the equation by : Simplifying this: So, the slope of this line is .
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The slope of a line perpendicular to this line is the negative reciprocal of . The negative reciprocal of is .
Thus, the slope of the perpendicular line is .
Would you like further explanation on any step?
Here are some follow-up questions:
- What is the slope of a line parallel to ?
- How do you find the equation of a line given its slope and a point?
- What is the negative reciprocal of ?
- How do you determine if two lines are perpendicular based on their equations?
- What does the slope tell you about the steepness of a line?
Tip: Always remember that perpendicular lines have slopes that multiply to give .
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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