8.3 Slope and intercepts
Between the graph of a linear equation and the equation itself, one can have two types of relationships I) The slope of the straight line II) Its intercepts.
Slope: In mathematics the word 'slope' has a specific meaning (see figure). Thus slope of segment MN is the ratio of the difference between y  coordinates of point M and N to the corresponding difference between their x  coordinates respectively.
Slope of segment MN =
Where x_{1} ¹ x_{2} means that the x  coordinates of both M and N should be different. But if x_{1} = x_{2} then the segment is parallel to y  axis i.e. it is a vertical segment which has no slope. Slope of any nonvertical segment can be always found. Slope of any line is the slope of any segment of it.
Note that :
 Slopes of parallel lines are equal.
The slopes of a line parallel to the x  axis and the x  axis itself is zero. (Horizontal lines).
The slope of a line parallel to the y  axis and the y  axis itself has no slope or this slope is undefined. (vertical lines).
 A line having a positive slope makes an acute angle with the positive direction of the x  axis.
A line having a negative slope, makes an obtuse angle with the positive direction of the x  axis.
The products of slopes of two mutually perpendicular lines is always 1 i.e. if two mutually perpendicular lines have slopes m_{1} and m_{2} respectively then
Example Find slope 'm' of the straight line through (3, 2) and (5, 2)
Solution : (x_{1}, y_{1}) = (3, 2) and (x_{2},y_{2}) = (5,2)
Therefore slope (m) =

Index
8.1 Definition 8.2
Relations, Graphs and Symmetry 8.3
Slopes and Intercepts
Chapter 9
