Exercise 35 Page 243

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+5y=10	y= -3/5x+2	m_1= -3/5
5x-3y=-6	y= 5/3x+2	m_2= 5/3

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 their slopes. If the product of the slopes equals - 1, then the lines are perpendicular.

m_1* m_2? =- 1

SubstituteII

m_1= -3/5, m_2= 5/3

-3/5 * 5/3? =- 1

MultFracByInverse

a/b* b/a=1

-1= -1

The slopes of the given lines are negative reciprocals, so the lines are perpendicular.