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)