Equation of Line in Normal Form
Equation of the line whose length of the perpendicular from the origin is p and the angle made by the perpendicular with the positive x-axis is given by α is given by:
x cos α + y sin α = p
This is known as the normal form of the line.
In the case of the general form of the line Ax + By + C = 0 can be represented in normal form as:
From this we can say that and
Also, it can be inferred that,
⇒
⇒
From the general equation of a straight-line Ax + By + C = 0, we can conclude the following:
- Slope is given by -A/B, given that B ≠ 0.
- x-intercept is given by -C/A and the y-intercept is given by -C/B.
- It can be seen from the above discussion that:
- If two points (x1, y1) and (x2, y2) are said to lie on the same side of the line Ax + By + C = 0, then the expressions Ax1+ By1 + C and Ax2 + By2 + C will have the same sign or else these points would lie on the opposite sides of the line.
Slope of a Line
Slope of a Line is the measure of the steepness of a line a surface or a curve whichever is the point of consideration. The slope of a Line is a fundamental concept in the stream of calculus or coordinate geometry or we can say the slope of a line is fundamental to the complete mathematics subject. The understanding of slope helps us solve many problems in mathematics, physics, or engineering.
In this article, we will learn about the slope of a line in detail, slope of a straight line with its various methods of calculations, and also the equation for the slope of a line.
Table of Content
- What is a Slope?
- What is the Slope of a Line?
- Slope of a Line Equation
- How to Find Slope of a Line?
- Calculation of Slope between Two Points
- Calculation of Slopes from Graph
- Calculation of Slope from Table
- Positive and Negative Slope
- Slopes of Different Lines
- Slope of Horizontal Line
- Slope of Vertical Line
- Slope of Perpendicular Lines
- Slope of Parallel Lines
- Equation of Line in Slope Intercept Form