There are number of forms of the equation of a line like the intercept form, the general equation of a line, the normalized equation, the Point slope equation, Slope intercept equation etc.
The equation of a standard line is given as
y = m x + c, where ‘m’ refers to the Slope of a line and ‘c’ refers the value of the y- intercept.
While finding the equations of lines we only needed to calculate the parameters ‘m’ and ‘c’. The value of ‘c’ can be calculated easily we just need to see that where the line crosses the y- axis.
To calculate the slopes of the equation of line just need to remember the formula shown below:
m = change in the ‘y’ parameter / change in the ‘x’ parameters = rise / run.
Some time these words Rise and run are used in spite of the parameters ‘y’ and ‘x’ respectively.
The point Slope of an equation of line is given as
y – y1 = m (x – x1)
m = (x – x1) / (y – y1)
Here x1 and y1 are the given point in the equation ‘m’ is the Slope of a line equation and (x, y) is any point located on the line.
The form of an equation of a line given above is similar to the equation of the Straight Line discussed in the starting. Basically in the point slope form the points (x1, y1) are actually the points (0, c) for the straight line equation.
Both forms can be interchanged with one another. Suppose we have
y – y1 = m (x – x1),
On putting the coordinates (0, b) in spite of (x1, y1), we get
y - b = m (x – 0),
y – b = mx,
y = mx + b.
Slope of a line is also known as gradient of line. Slope of a line represents the Ratio of change in ‘Y’ to change in ‘X’ between two points on a line. If the Slope of line is undefined or not defined then it is said to be a vertical line and if the Slope of line is 0, then it is said to be a horizontal line.
Now we will see Equation of a line: