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:
y = mx + c
Where ‘m’ define Slope of a line and the y- intercept is given by ‘c’.
Slope of a line can be defined by using the following formula:
m = u1
‘m’ is the slope of line and u1,
are the points on y- axis and v1,
are the points on x- axis.
The above equation can also be described as:
m = u2
The gradient of a line can be represented by following formula:
We can understand slope with help of an example:
Assume that a line follows two points: A = (3, 3) and B = (7, 5), therefore by the division of the change in y - coordinate by the change in x - axis, one can easily calculate the slope of the line:
The formula for finding the slope of a line is:
m = u2– u1/v2 – v1
= 7 – 3 / 5 – 3
= 4 / 2
This is how we Define slope of a line;
If the slope of a line is equal to -1, then two lines are perpendicular to each other.