Equation of Line Using Slope
If a line is passing through a point (x1, y1) and its slope is m, then the equation of a line is given as follows:
y – y1 = m(x – x1)
Where x and y represent all the coordinates of the line.
We can also write the same equation using the two points from which the line is passing. If the line passes through (x1, y1) and (x2, y2) then its equation is given by:
Example 1: Find the equation of a line given in the graph.
Solution:
Slope of the graph is, m = 8/2 = 4
and we know the equation of line passing through (x1, y1) with slope m is given by
y – y1 = m (x – x1)
Thus, equation of line (4,2) with slope 4 is
y – 2 = 4 (x – 4)
⇒ y – 2 = 4x – 16
⇒ y = 4x – 16 +2
⇒ y = 4x – 14
Example 2: Find the equation of the line given in the graph.
Solution:
Two given points (x1, y1) and (x2, y2) are A (2,3) and B (5,7)
⇒ y-3= {(7 -3)/(5-2)} (x-2)
⇒
⇒
⇒ 3y-9 = 4x-8
⇒ 3y = 4x+1
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