Final answer:
The relationship between line equations can be determined by analyzing their slopes. Lines with the same slope are parallel, and lines with slopes that are negative reciprocals are perpendicular. Line A and Line B have slopes that are negative reciprocals, indicating they are perpendicular.
Step-by-step explanation:
When discussing the relationship between line equations, we focus on their slopes and y-intercepts, as expressed in the general form y = mx + b, where m is the slope and b is the y-intercept. If two lines have the same slope, they are parallel to each other. When lines have slopes that are negative reciprocals of each other, they are perpendicular, forming a 90° angle. The relationship between lines in a Cartesian plane dictates whether they are parallel, perpendicular, or intersect at a point.
Considering the slopes provided:
- Line A has a slope of -4.7
- Line B has a slope of 12.0
The slopes of Line A and Line B are negative reciprocals of each other (-4.7 and 1/-4.7 = 12.0 approximately), indicating that the lines are perpendicular. Perpendicular lines form a 90° angle with each other. This is because the product of their slopes equals -1 (-4.7 * 12.0 = -56.4, which is close to -1 if we do not round the values). The equations of the lines represent a linear relationship between two variables, and analyzing these slopes is critical for understanding how the lines interact within a coordinate system.