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Straight Line

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A straight line is a one-dimensional figure. It has no breadth or height. It is just an extension of a point. A straight line is an endless length which does not bend in any direction. A line has an infinite length, whereas a line segment is a portion of line bounded between two points. A line segment can be referred as the shortest distance between two points.

Straight line is not just a small concept as it appears. In fact, it is the foundation of many other axioms and theorems.

Straight Line Definition

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A straight line can be defined as a run of a point in a fixed direction. It is a one-dimensional image with no breadth and depth. A straight line is an extension of a point in either direction and is represented by a line with arrows at its ends as shown below:
Straight Line
A line segment is defined as the shortest distance between two points. Following figure shows a straight line:
Line Segment
A ray is a form of straight line which is an extension of a point in one direction only. A ray is drawn below:
Ray

Equation of a Straight Line

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There are various equations of straight line.
General Equation of a Straight Line:
General Equation of a Straight Line
Where, $A\neq 0$ and $B\neq 0$.
Slope-Intercept Form:
Slope-Intercept Form
Where, m = Slope (inclination of the line from the horizontal)
and c = y intercept.
Point Form:
Point Form
Where, (x1,y1) is the point lying on the line.
Point-Slope Form:
Point-Slope Form
Where, m = Slope
and (x1, y1) is a point lying on the line.

Straight Line Construction

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Following steps to be followed while graphing a straight line:
Step 1: Convert the equation in slope-intercept form if it is not.
Step 2: Compare it with slope-intercept form, y = mx + c, and determine the value of m and c.
Step 3: Find the rise and run. Numerator of the slope is known as rise and denominator is called run.
Step 4: Locate y intercept (the value of "c") on the graph.
Step 5: Assuming this point as center, locate rise by moving up or down on y axis according to the positive or negative sign of rise.
Step 5: Now, from this point, run left or right horizontally according to the positive or negative sign of run.
Step 6: Join point obtained by y intercept and point obtained by locating slope. The required line is obtained.
Let us take an example.

Solved Example

Question: Graph the line $2x+3y=3$.
Solution:
$2x+3y=3$
$3y=-2x+3$

$y=-$$\frac{2}{3}$$x+1$

$m=-$$\frac{2}{3}$

Rise = -2
Run = 3
c = 1
The following graph is obtained after locating y intercept, rise and run:
Straight Line Construction

Straight Line Distance

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We can find the distance between two points located on a straight line.
Straight Line Distance
Formula for distance of a straight line bounded between two points is given below:
Straight Line Distance Formula
Where, (x1, y1) and (x2, y2) are two endpoints of a straight line and d is the distance between them.