Slope of Line

Slope review | Algebra (article) | Khan Academy

The slope of a line refers to the steepness or inclination of a straight line. In the coordinate plane, the slope of a line can be determined with the help of two different points lying on the line. The slope or steepness of a line is measured by the nature of change in y-values corresponding to the change in x-values of any two points on the line.

Definition of the Slope of a Line

The slope of a line is defined by the change in y-coordinate with respect to the change in x-coordinate between two points on the line. It is measured as the ratio of the difference in y-coordinate and the difference in x-coordinate values. The change in x values is called run and the change in y values is called rise. 

For example, if two points on a straight line have coordinates as (x1, y1) and (x2, y2) respectively, then the slope of the line is defined as m = (y1 – y2)/(x1 – x2). 

Types of the Slope of a Line

The slope can be of different types depending on the value of m. These are explained as follows:

  • Positive slope: The slope of a line is positive means with an increase in values of x, the value of y also increases. The line with a positive slope rises as we move from left to right along the x-axis.
  • Negative slope: The slope of a line is negative when the value of y decreases with an increase in the value of x. This type of line falls as we move from left to right along the x-axis.
  • Zero slope: Thi slope of a line is zero means the change in y values is zero with an increase in the value of x. It signifies a horizontal line parallel to the x-axis in which y values remain unchanged with a change in x values.
  • Undefined slope: The slope becomes undefined when a change in x values is zero which means all y values on the line correspond to only one x value. This indicates a vertical line parallel to the y-axis.

Equation of Line Using Slope Value

The equation of a straight line can be written if the slope of the line is known. The equation of a straight line is denoted by the expression y = mx + b

Here, m denotes the slope of the line and b denotes the y-intercept (the point on the y-axis where the line meets the y-axis)

For a straight line equation y = 2x -7, the slope is 2 and for the straight line y = -9x + 15, the slope is -9.

If two straight lines have the same slope value, then these two lines are parallel to each other.

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