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Chapter 9: Problem 37

In Exercises \(33-38\), determine whether the lines with the given equations are parallel, perpendicular, or neither. \(2 x+1=0\) \(-3 y-4=0\)

Short Answer

Expert verified
Perpendicular

Step by step solution

01

Rewrite the first equation in slope-intercept form

The equation given is \(2x + 1 = 0\). Solve for \(x\) to get it in the form \(x = \text{constant}\), \(2x = -1 \) therefore, \(x = -\frac{1}{2} \). This equation represents a vertical line, which does not have a defined slope.
02

Rewrite the second equation in slope-intercept form

The equation given is \(-3y - 4 = 0\). Solve for \(y\) to get it in the form \(y = mx + b\), \(-3y = 4\), so \(y = -\frac{4}{3}\). This equation represents a horizontal line with a slope of zero.
03

Determine the relationship between the lines

A vertical line is always perpendicular to a horizontal line. Therefore, the lines represented by the equations \(2x + 1 = 0\) and \(-3y - 4 = 0\) are perpendicular.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

slope-intercept form
The slope-intercept form is a way of writing the equation of a line so that you can easily identify its slope and y-intercept. The general form is \( y = mx + b \), where:
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Most popular questions from this chapter

Find the midpoint of the line segment between the points given. Plot the points \(A(3,-2), B(6,-5),\) and \(C(2,-6) .\) Connect the points to form a triangle. a. Calculate the length of each side of the triangle. b. What kind of triangle is it? Justify your answer.

In Exercises \(7-24,\) find the general form of the equation of the line satisfying the conditions given and graph the line. Through \((-2,-4)\) with slope \(-3\)

Find the general form of the equation of the line passing through \((4,-7)\) and perpendicular to the line with equation \(x-5 y+7=0\)

In Exercises \(7-24,\) find the general form of the equation of the line satisfying the conditions given and graph the line. Through \((-7,1)\) and \((3,-5)\)

Find the slope-intercept form of the equation of the line passing through the points \((4,-5)\) and \((2,8) .\) What is the slope? the \(y\) -intercept?
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