Lesson 3 of 10 · 10 min
Slope from two points
NCERT §9.2.1
Riya marks two points of the canal, (2, −5) and (6, −2), but she has no protractor. Can she still find its slope?
The lesson in notes
In short
A non-vertical line through P(x₁, y₁) and Q(x₂, y₂) has slope m = (y₂ − y₁)/(x₂ − x₁), with x₁ ≠ x₂. The same result holds whether the inclination is acute or obtuse.
The order of the points does not matter, as long as it is the same in top and bottom: from (1, 2) to (4, 8) the slope is 6/3 = 2, and from (4, 8) to (1, 2) it is (−6)/(−3) = 2.
Through (3, −2) and (−1, 4): m = 6/(−4) = −3/2. Through (3, −2) and (7, −2): m = 0/4 = 0, a horizontal line.
Through (3, −2) and (3, 4) the run x₂ − x₁ is 0, so the slope is not defined: the line is vertical.
Three points A, B, C are collinear exactly when the slope of AB equals the slope of BC. For (1, 1), (2, 3), (4, 7) both slopes are 2.