Math 1 · Unit 4 · Lesson 1 · part 3 of 6
Write a parallel line through a point
The main skill: given a line, write the equation of a line parallel to it through a given point .
Write a parallel line through a point
The main skill: given a line, write the equation of a line parallel to it through a given point. Two moves, and both come from Unit 3.
- 1Keep the slopeParallel means the same m. Read m off the given line (rewrite it into y = mx + b first if you have to).
- 2Use the point to find the new bPut the point's x and y into y = mx + b with the kept m, and solve the one-step equation for b. Then write y = mx + b.
Worked: parallel to y = 2x − 5 through (3, 4)
Keep m = 2.
Put in (3, 4): 4 = 2 × 3 + b, so 4 = 6 + b. Add −6 to both sides: b = −2.
y = 2x − 2. Check: 2 × 3 − 2 = 4. Yes. Same tilt as the original, slid down 3.
Worked: parallel to 3x + y = 7 through (−2, 1)
Rewrite first: y = −3x + 7, so m = −3. Keep it.
Put in (−2, 1): 1 = −3 × (−2) + b, so 1 = 6 + b, so b = −5.
y = −3x − 5.
Two special casesAny two vertical lines are parallel: x = 2 and x = 5 both go straight up and down and never meet. They have no slope, so you cannot compare m; you see it by sight. Any two horizontal lines are parallel too: y = 1 and y = 4 both have slope 0.