Question

Based on each situation, select the correct number of solutions and description of the corresponding graph.
Situation Number of Solutions Description of Graph
Two lines that have the same slope and y-intercept
no solution

one solution

infinitely many solutions

parallel lines

lines intersect at one point

same line

Two lines that have different slopes but the same y-intercept
no solution

one solution

infinitely many solutions

parallel lines

lines intersect at one point

same line

Two lines that have the same slope but different y-intercepts
no solution

one solution

infinitely many solutions

parallel lines

lines intersect at one point

same line

Answer 1

Two lines that have the same slope and y-intercept
- Number of solutions: infinitely many
- Description: same line (coincident lines)

Two lines that have different slopes but the same y-intercept
- Number of solutions: one solution
- Description: lines intersect at one point

Two lines that have the same slope but different y-intercepts
- Number of solutions: no solution
- Description: parallel lines

(Reason: identical lines give infinitely many common points; distinct nonparallel lines meet exactly once; equal slopes with different intercepts are distinct parallel lines and never meet.)