Lessons · Quantitative Reasoning
CLT Quantitative Reasoning · Lesson
Lines and slope
Slope is rise over run: (y₂ − y₁) ÷ (x₂ − x₁). A line is y = mx + b, where m is the slope and b is where it crosses the y-axis.
- Find the slope from two points.
- Put one point into y = mx + b to find b.
- Parallel lines have equal slopes; perpendicular slopes are negative reciprocals (2 and −½).
Q. What is the equation of the line through (1, 2) and (3, 8)?
Answer y = 3x − 1
Slope = (8 − 2) ÷ (3 − 1) = 3. Then 2 = 3(1) + b, so b = −1. Check with (3, 8): 3(3) − 1 = 8.
- Subtracting the x-values in the opposite order from the y-values.
- Giving the reciprocal without the sign change for a perpendicular line.
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