Final answer:
Line g with a slope of -4/5 and line h with a slope of 5/4 are perpendicular because their slopes are negative reciprocals of each other, their product is -1. Hence, the correct answer is D. Yes, because the slopes of lines g and h are opposite and reciprocal.
Step-by-step explanation:
To determine if two lines are perpendicular, we need to compare their slopes. Two lines are perpendicular if and only if the product of their slopes is -1, meaning that the slopes are negative reciprocals of each other. For the lines described:
- Line g: y = -4/5x + 7/5 has a slope of -4/5.
- Line h: y = 5/4x + 3/4 has a slope of 5/4.
By multiplying the slopes of line g and line h:
-4/5 × 5/4 = -1
Since the product of the slopes is -1, line g is indeed perpendicular to line h. The correct answer to whether line g is perpendicular to line h is: D. Yes, because the slopes of lines g and h are opposite and reciprocal. Answer option A is incorrect because although line g and h are perpendicular, the reasoning that 'the y-intercepts are different' is not a criterion for perpendicularity. Options B and C are both incorrect as they do not correctly identify the relationship between the slopes of perpendicular lines.