Parallel and perpendicular lines, step by step
Parallel lines have equal slopes; perpendicular slopes are negative reciprocals.
The question
Write the equation of the line through (−2, −2) parallel to y = 3x + 3.
Write the equation of the line (−2, −2), // y = 3x + 3
y = 3x + 3
m=3
b = −2 − (3)(−2)=4
y = 3x + 4
- Parallel lines have equal slopes, so read the slope straight off the given line: y = 3x + 3 has slope 3, and so does the new line.
- Now use the point. Put it back in to find b: b = y − mx = −2 − (3)(−2) = 4.
- Write it as y = mx + b: y = 3x + 4.
How it works.
- 01
Parallel lines have equal slopes, so read the slope straight off the given line: y = 3x + 3 has slope 3, and so does the new line.
- 02
Now use the point. Put it back in to find b: b = y − mx = −2 − (3)(−2) = 4.
- 03
Write it as y = mx + b: y = 3x + 4.