Final answer:
The parallel slope to -2/7 is also -2/7, and the perpendicular slope is the negative reciprocal, which is 7/2. These properties are based on the fact that parallel lines have equal slopes, and perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
The slope of a line is represented by m in the slope-intercept equation of a straight line, which is y = mx + b. For two lines to be parallel, their slopes must be equal. Therefore, the parallel slope to a line with a slope of -2/7 is also -2/7.
For two lines to be perpendicular, their slopes must be negative reciprocals of each other. The negative reciprocal of -2/7 is obtained by flipping the fraction and changing the sign, which results in 7/2.
Parallel and Perpendicular Slopes
- Parallel slope: -2/7
- Perpendicular slope: 7/2
These concepts are crucial when analyzing the relationship between lines on a Cartesian plane. A visual representation of these concepts can be seen in Figure A1 of the Slope and the Algebra of Straight Lines, which shows how the slope determines the steepness of the line and how the slope remains constant along a straight line.