A straight line is a curve, where every point on the line segment joins any two points lying on it. So, every first degree equation in x and y represents a straight line. There is always a fixed relationship between the x and y coordinates of any points on the line. For example: x + y = 0, 4x + y = 0, y = 0. 
A and B are the coefficients of x and y respectively. The ordered pair r = (x, y) can be defined as a point.
Standard form of equation is mainly used under the following circumstances:

When we want to graph a line

When we want to know the yintercept of the line
 When we want to know the xintercept
The general formula of equation of line passing through a point ($x_1,y_1$) and having slope m is given as
Here, 'm' is the slope of the line
x_{1} is the Coordinate of xaxis
y_{1} is the Coordinate of yaxis
Here are few solved example on the equation of line:
Solved Examples
Solution:
(x_{1}, y_{1}) <> (4, 5)
Using the formula of the equation of line, we get
$yy_{1}$ = $m(xx_{1})$
y  5 = 7(x  4)
y  5 = 7x  28
7x  y  28 + 5 = 0
7x  y  23 = 0
This is the required equation of line.
Solution:
(x_{1}, y_{1}) <> (8, 9)
Using the formula of equation of the line, we get
$yy_{1}$ = $m(xx_{1})$
(y  9) = 3( x  8 )
y  9 = 3x  24
3x  y  24 + 9 = 0
3x  y  15 = 0
Where, m is the slope of the line and b is the yintercept and x and y are the coordinates of any point on the line.
Slope (m) is the 'steepness' of the line and 'b' is the intercept, that is the point where the line crosses the yaxis.
This equation of the line is mainly used in the following circumstances:

To define a particular line in an accurate way.

To locate the points on the line.
Solved Examples
Solution:
m = 7 and b = 4
Using the formula y = mx + b, we get
y = 7x + 4
7x  y + 4 = 0
$\therefore$ The equation of the line is 7x  y + 4 = 0
Step 2: Given:
m = 7 and b = 4
Using the formula y = mx + b, we get
y = 7x + 4
7x  y + 4 = 0
$\therefore$ The equation of the line is 7x  y + 4 = 0
Solution:
m = 0.2 and c = 7
Using the formula y = mx + c, we get
y = 0.2 (x) + 7
y = $\frac{x}{5}$ + 7
5y = x + 35
x  5y + 35 = 0
$\therefore$ The equation of the line is x  5y + 35 = 0.
Therefore, any point of line can be reached by the radius vector