Lesson 2 of 10 · 6 min
Slope of a line
NCERT §9.2
Riya's canal leans across the sheet. To describe how steep a straight line is, which single number should she use?
The lesson in notes
In short
The inclination θ of a line is the angle it makes with the positive x-axis, measured anticlockwise, so 0° ≤ θ ≤ 180°. A line parallel to the x-axis has θ = 0°; a vertical line has θ = 90°.
The slope (or gradient) of a non-vertical line is m = tan θ. The slope of a vertical line (θ = 90°) is not defined.
The x-axis has slope 0; the y-axis has no slope. A line inclined at 60° has slope tan 60° = √3, at 45° slope 1, and at 135° slope −1.
An acute inclination gives a positive slope: the line rises from left to right. An obtuse inclination gives a negative slope: the line falls.
Slope tells how steep the line is: a slope of 2 means that for every 1 unit moved to the right the line goes up 2 units.