Chapter 10.2, Problem 21E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In Exercises 21 to 24, state whether the lines are parallel, perpendicular, the same (coincident), or none of these.*

To determine

**To check:**

The relationship between the lines

Explanation

Initially check the given equation,

If the one equation is derived from other, then these lines are same or coincident in nature.

The two given equations

If not, then proceed with the following procedures.

By theorem,

If two lines are parallel, then their slopes are equal.

(i.e) If

If two lines are perpendicular, then the product of their slopes is

(i.e) If

To find the relation between the lines, the slopes of the lines are needed.

Thus we need to find the points on the lines.

Let

The slope of the line that contains the points

The points of the line

Substitute

On simplifying,

The coefficient of

Thus the first point is

Substitute

The coefficient of

On simplifying,

Thus the second point is

The line

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