Lines, Functions, Systems Identifying parallel and perpendicular lines from equations
The equations of three lines are given below.
Line 1: $y=2 x-7$
Line 2: $6 x-3 y=-12$
Line 3: $y=2 x-2$
For each pair of lines, determine whether they are parallel, perpendicular, or $\mathrm{n}$
Line 1 and Line 2:
Line 1 and Line 3:
Line 2 and Line 3 :
Parallel
Parallel
Parallel
Perpendicular
Perpendicular
Perpendicular
Neither
Neither
Neither
Answer
Comparing Line 2 and Line 3, both lines have the same slope of 2. Therefore, Line 2 and Line 3 are parallel.
Step 1 ：The slope of Line 1 is 2.
Step 2 ：The slope of Line 2 is also 2.
Step 3 ：The slope of Line 3 is 2.
Step 4 ：Comparing Line 1 and Line 2, both lines have the same slope of 2. Therefore, Line 1 and Line 2 are parallel.
Step 5 ：Comparing Line 1 and Line 3, both lines have the same slope of 2. Therefore, Line 1 and Line 3 are parallel.
Step 6 ：Comparing Line 2 and Line 3, both lines have the same slope of 2. Therefore, Line 2 and Line 3 are parallel.
