Straight line was introduced by ancient mathematicians to represent straight objects.Straight line is a line traced by a point traveling in a constant direction. In geometry, a line is always considered as a straight line. It has a breadth less length and there will be no curves. Different types of lines are tangent lines, secant lines, exterior lines etc..

A line segment is a part of a line bounded by two distinct end points and contains every point on the line between its end points. Two or more line segments can be parallel, intersecting or skewed.

## Equation of a Straight Line

The general form of a straight line is defined by a linear equation,
Ax + By + C = 0
where, A and B are non zero

Slope - Intercept form

y = mx + c
m : Slope or gradient
c : y - intercept
y : how far up
x : how far along

The above equation is obtained from the point-slope equation ( y = m (x - a) + c) by setting a = 0. Point slope equation can be written for any point on the line as it is not unique. However, slope intercept equation is said to be unique and has two parameters; slope and y - intercept.

Given below is an example of a straight line:

### Solved Example

Question: Find the slope and y-intercept for the equation 3y = -12x + 15
Solution:

Consider the given equation  3y = -12x + 15

Solve for y

y = -4x + 5   -----1

The equation of slope - intercept is of the form:  y = mx + c

Comparing the equation 1 with the slope-intercept form
we get Slope(m) = -4
y - intercept(c) = 5

## Straight Line Graph

A straight line is formed by joining the starting point and the ending point.
Given below is an example of a straight line graph.

### Solved Example

Question: Construct a straight line for the equation y = 2x + 3
Solution:

The given equation is a linear equation. As the given equation represents the equation of a straight line we wish to graph y = 2x + 3 by determining two points.

To determine two points we find the value of y by choosing x = 2

So when x = 2 in the given equation, y = 7

We have our first point as (2, 7)

Now to find the second point let us choose x = 1 then y = 5

Therefore the second point is (1, 5).
Since the two points are now obtained we can draw a straight line through them.

 x 2 1 y 7 5

## Straight Line Distance Formula

Consider two points A and B  having coordinates ($x_{1}, y_{1}$) and ($x_{2}, y_{2}$) respectively.  For the straight line AB distance formula is given by

d = $\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }$
($x_{1}, y_{1}$) are the (x, y) coordinates for one point.
($x_{2}, y_{2}$) are the (x, y) coordinates for the second point.
d: Distance between two points.

### Solved Example

Question: Find the distance between the points (5, 2) and (4, 9)
Solution:

Let ($x_{1}, y_{1}$) = (5, 2) and ($x_{2}, y_{2}$) = (4, 9)

The distance formula is given by
d = $\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }$
Plug in the given values

d = $\sqrt{( 4 - 5)^{2} + (9 - 2)^{2} }$
d = $\sqrt{(-1)^{2} + (7)^{2}}$
d = $\sqrt{50}$
d = 7.07 (approx)