Table of Contents
What is a Slope?
A slope is a mathematical term that describes the steepness, or incline, of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate, and is usually expressed as a ratio or percentage. For example, if a line has a slope of 2, that means for every increase of 2 in the x-coordinate, there is a corresponding increase of 1 in the y-coordinate.
Slope Equation
The slope equation states that the slope of a line is equal to the change in y-coordinates divided by the change in x-coordinates.
Equation of a Straight Line
The equation of a straight line is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is the change in y divided by the change in x, and the y-intercept is the point at which the line crosses the y-axis.
Equation of a Line Example
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
In the example below, the slope is 3 and the y-intercept is 1.
y = 3x + 1
How to Find Equation of Line Passing Through Two Given Points?
To find equation of line passing through two given points, we use the point-slope form of the equation of a line. This form is:
y = mx + b
Where:
m is the slope of the line
b is the y-intercept of the line
To find the equation of a line passing through two points, P1(x1, y1) and P2(x2, y2), we simply plug in the coordinates of both points into the point-slope form equation.
For example, if we want to find the equation of the line passing through the points (2, 3) and (5, -1), we would plug in these coordinates into the equation:
y = mx + b
y = (3)x + (0)
y = 3x
Line Perpendicular to a Line
To find the equation of a line perpendicular to a given line, use the following steps:
1. Write the equation of the given line.
2. Use the slope of the given line to find the slope of the perpendicular line.
3. Use the slope of the perpendicular line to find the equation of the perpendicular line.
