Question

what feature do parallel lines share in a coordinate plane?

a. same slope

b. same width

c. same y-intercept

d. same length

Explanation:

To determine the feature parallel lines share in a coordinate plane, we analyze each option:

• Option a: In the coordinate plane, the slope of a line determines its steepness and direction. Parallel lines have the same steepness and direction, so they have the same slope. For example, the lines \( y = 2x + 1 \) and \( y = 2x + 3 \) are parallel and both have a slope of 2.
• Option b: "Width" is not a defined property for lines in the context of a coordinate plane related to parallelism. Lines are one - dimensional and do not have width in this sense.
• Option c: If two lines have the same y - intercept, they intersect at the point where \( x = 0 \), so they are not parallel (unless they are the same line). For example, \( y=2x + 1\) and \( y = 3x+1\) intersect at \( (0,1) \) and are not parallel.
• Option d: Lines in a coordinate plane are infinite in length, and the concept of "same length" is not applicable to parallel lines as they are not measured by length in the context of their parallelism.

Answer:

a. Same slope