Exercise 11 Page 184

Lines are parallel if their slopes are identical, and perpendicular if their slopes are negative reciprocals. Any other relationship between the lines would be neither parallel nor perpendicular. Let's write each equation in slope-intercept form, highlighting their slopes.

Given Equation	Slope-intercept form	Slope
2x + 6y = -12	y= -1/3x + (-2)	m_1= -1/3
y=3/2x - 5	y= 3/2x + (-5)	m_2= 3/2
3x-2y=-4	y= 3/2x+2	m_3= 3/2

We can see that lines b and c have the same slope. Therefore, these lines are parallel. To determine whether or not the lines are perpendicular, we calculate the product of the slopes. Any two slopes whose product equals - 1 are negative reciprocals, and therefore the lines will be perpendicular. Let's start with lines a and b.

m_1* m_2? =- 1

SubstituteII

m_1= - 1/3, m_2= 3/2

( - 1/3) * 3/2? =- 1

MultNegPos

(- a)b = - ab

- 1/2≠ - 1 *

The product of the slope does not equal -1, so we know that lines a and b are not perpendicular. Since lines b and c are parallel, lines a and c cannot be perpendicular.