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McGraw Hill Glencoe Algebra 1, 2012 View details

4. Parallel and Perpendicular Lines

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Exercise 36 Page 243

How do you know if lines are parallel or perpendicular?

Neither

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Lines are parallel if their slopes are exactly the same, and perpendicular if their slopes are negative reciprocals. Any other relationship between the slopes would result in neither parallel nor perpendicular lines. Let's write both equations in slope-intercept form, highlighting their slopes.

Given Equation	Slope-intercept form	Slope
-3x+4y=8	y= 3/4x+2	m_1= 3/4
-4 x+3y=-6	y= 4/3x-2	m_2= 4/3

Since the lines have different slopes, we can conclude that they are not parallel. To determine whether they are perpendicular or not, we will calculate the product of the slopes. If the product of the equals - 1, then the lines are perpendicular.

m_1* m_2? =- 1

SubstituteII

m_1= 3/4, m_2= 4/3

3/4 * 4/3? =- 1

MultFracByInverse

a/b* b/a=1

1≠ - 1

The lines are neither parallel nor perpendicular.

Subchapter links

Check Your Understanding p.242

Practice and Problem Solving p.243-244

H.O.T. Problems p.244

Standardized Test Practice p.245

Spiral Review p.245

Skills Review p.245

Exercise 36 Page 243

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