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Chapter 3: Problem 56

If two lines are perpendicular, describe the relationship between their slopes.

Short Answer

Expert verified
The slopes of two perpendicular lines are negative reciprocals of each other, i.e., the product of their slopes is -1. If the slope of one of the lines is 0, the other line (being vertical) has an undefined slope.

Step by step solution

01

Definition of Perpendicular Lines

Perpendicular lines are two lines that intersect at a right angle (90 degrees). In a Cartesian Plane, this can be visualized as two lines where if one line is sloping upwards, the other line is sloping downwards.
02

Understanding Slope

The slope of a line in a coordinate plane is obtained using the formula \( m = \Delta y / \Delta x \); where \( \Delta y \) is the change in y-coordinates and \( \Delta x \) is the change in x-coordinates. It basically tells us about the steepness of the line.
03

Relating Slopes of Perpendicular Lines

For two lines to be perpendicular, the product of their slopes should be -1. In other words, if one line has slope m1 and the other line has slope m2, then \( m1 x m2 = -1 \). If the slope of one of the lines is 0 (making it horizontal), then the other line, being vertical, has an undefined slope.

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Most popular questions from this chapter

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((2,4)\) and has the same \(y\) -intercept as the line whose equation is \(x-4 y=8\)

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((-6,4)\) and is perpendicular to the line that has an \(x\) -intercept of 2 and a \(y\) -intercept of \(-4\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If I could be absolutely certain that I have not made an algebraic error in obtaining intercepts, I would not need to use checkpoints.

What does it mean if the slope of a line is zero?

A college campus goes beyond the standards described in Exercise \(49 .\) All wheelchair ramps on campus are designed so that every vertical rise of 1 foot is accompanied by a horizontal run of 14 feet. What is the grade of such a ramp? Round to the nearest tenth of a percent.
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