What you’ll learn
Write equations of parallel lines.
Key idea
Parallel lines keep the slope; the specified point determines the new intercept.
Equal slope alone does not ensure the specified point or distinctness; output is not automatically intercept.
Worked example
Enter the exact value or ordered values in the format requested below.
A reference path on a coordinate map is y=-5x-5. A distinct parallel path must pass through (4,-28). Write the full target equation.
- Parallel distinct paths have equal finite slope -5 but different intercepts.
- -28=-5(4)+b gives b=-8, distinct from -5; target y=-5x-8 passes through the designated point.
Answer: y=-5x-8
Quick Check
Choose which candidate representation satisfies the requirements of 'Write equations of parallel lines' and justify the choice.
A reference path on a coordinate map is y=-5x-5. A distinct parallel path must pass through (-4,17). Choose with BOTH parallelism and point evidence.