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 x1 ¹ x2 means that the x - coordinates of both M and N should be different. But if x1 = x2 then the segment is parallel to y - axis i.e. it is a vertical segment which has no slope. Slope of any non-vertical 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 m1 and m2 respectively then
Example Find slope 'm' of the straight line through (-3, 2) and (5, -2)
Solution : (x1, y1) = (-3, 2) and (x2,y2) = (5,-2)
Therefore slope (m) =
Relations, Graphs and Symmetry
Slopes and Intercepts