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- Quadratic Equations
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Equation of a Line
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- Concept of Slope (or, gradient)
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Similarity
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Estimated time: 5 minutes
- Slope of a Line Or Gradient of a Line.
- Parallelism of Line
- Perpendicularity of Line in Term of Slope
- Collinearity of Points
- Slope of a line when coordinates of any two points on the line are given
- Conditions for parallelism and perpendicularity of lines in terms of their slopes
- Angle between two lines
- Collinearity of three points
Maharashtra State Board: Class 12
CISCE: Class 10
CISCE: Class 10
Definition: Slope
The slope m of a line is m = tanθ
where θ is the inclination of the line with the positive x-axis.
Maharashtra State Board: Class 12
CISCE: Class 10
CISCE: Class 10
Formula: Slope Between Two Points
\[m=\frac{y_2-y_1}{x_2-x_1}\]
Maharashtra State Board: Class 12
CISCE: Class 10
CISCE: Class 10
Key Points: Concept of Slope
Nature of Slope
-
m > 0 → rising line
-
m < 0 → falling line
-
m = 0 → horizontal line
-
m = ∞→ vertical line
Parallel Lines
Two lines are parallel ⇔ , their slopes are equal, m1 = m2
Perpendicular Lines
Two lines are perpendicular ⇔
Collinearity of Three Points
Points A, B, and C are collinear
Method 1: Distance method
AB + BC = AC
Method 2: Slope method
Slope of AB = Slope of BC
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Related QuestionsVIEW ALL [124]
| Column C1 | Column C2 |
| (a) The coordinates of the points P and Q on the line x + 5y = 13 which are at a distance of 2 units from the line 12x – 5y + 26 = 0 are |
(i) (3, 1), (–7, 11) |
| (b) The coordinates of the point on the line x + y = 4, which are at a unit distance from the line 4x + 3y – 10 = 0 are |
(ii) `(- 1/3, 11/3), (4/3, 7/3)` |
| (c) The coordinates of the point on the line joining A (–2, 5) and B (3, 1) such that AP = PQ = QB are |
(iii) `(1, 12/5), (-3, 16/5)` |
