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.
Simulations in this lesson
Each on its own page