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  1. Glossary
  2. /Mathematics
  3. /Slope of a Line

What is Slope of a Line?

In short

The slope of a line is its steepness: the change in yyy divided by the change in xxx between any two points, m=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

In simple words

A line that rises from left to right has a positive slope. A line that falls has a negative slope. A horizontal line has slope 000, and a vertical line has no slope defined. The equation y=mx+cy = mx + cy=mx+c gives the slope mmm and the yyy-intercept ccc. Two lines are parallel if their slopes are equal and perpendicular if the product of the slopes is −1-1−1.

Example

Through (1,2)(1, 2)(1,2) and (4,8)(4, 8)(4,8) the slope is m=8−24−1=2m = \dfrac{8 - 2}{4 - 1} = 2m=4−18−2​=2, so the line is y−2=2(x−1)y - 2 = 2(x - 1)y−2=2(x−1), which is y=2xy = 2xy=2x.

Learn it properly

  • Lessons on this topic
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Related terms

  • Function
  • Pythagoras Theorem

← All glossary terms

Learn it in

  1. Slope and Equations of Straight LinesClass 11 to 12
  2. General Form, Distances and Families of LinesClass 11 to 12
All lessons on this topic →

Practise

  1. The origin is moved to the point (3, -2)…Medium
  2. For every number k, the line (1 + 2k)x + (2 - k)y - (8 + k) = 0 passes through the same…Hard
Find the line through the meeting point of x + 2y - 5 = 0 and 3x - y - 1 = 0 that also…Medium
  • A triangle has vertices (2, 1), (8, 9) and (10, 3), with coordinates in cm…Medium
    • All problems on this topic →

    Quick questions

    1. A line through the meeting point of x + y - 3 = 0 and 2x - y = 0 is parallel to 6x + 8y…Hard
    2. The origin is shifted to (1, -2). The line 3x - 2y + 8 = 0 becomesMedium
    3. The points (1, 2) and (3, 4) lie on opposite sides of the line 2x - y + k = 0 exactly whenHard

    More Mathematics terms

    1. Algebraic Identity
    2. Arithmetic Progression
    3. Complex Number
    4. Derivative
    5. Isosceles Triangle
    6. Linear Equation
    All Mathematics terms →

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