Find the slope of a line, and derive its equation using point-slope and two-point forms, plus conditions for parallel and perpendicular lines.
The slope between two points (x₁,y₁) and (x₂,y₂) is (y₂−y₁)/(x₂−x₁). The equation y−y₁=m(x−x₁) gives a line's equation from a point and slope.
Find the slope of the line through (2,3) and (6,11).
(11−3)/(6−2)=8/4=2
Find the equation of the line with slope 3 passing through (1,2).
y−2=3(x−1) → y=3x−1
Two lines are parallel if their slopes are equal. Two lines are perpendicular if the product of their slopes is −1.
A line has slope 4. Find the slope of a line parallel to it.
4 (parallel lines have equal slopes)
A line has slope 2. Find the slope of a line perpendicular to it.
−1/2, since 2×(−1/2)=−1
1. Find the slope of the line through (0,0) and (5,10).
2. Find the equation of the line with slope −2 through (3,4).
3. Find the equation of the line through (1,1) and (4,7).
4. A line has slope 5. Find the slope of a line perpendicular to it.
5. Two lines have slopes 3 and 3. Are they parallel, perpendicular, or neither?