Introduction to Equations of straight lines

Introduction to Equations of straight lines:

A straight line is representing by an equation of the first degree in two variables (x and y). Equally locus of an equation of the first degree in two variables is a straight line.

Equations of straight lines are used to the following forms:

Specify the slope and the "y intercept ->b", of the line.
Specify the slope of the line and one point on the line.
Specify two points through which the line passes.

Discussion on Equations of Straight Lines

The "y intercept ->b", slope m and the equation of the straight line is

y = m x + b

If the slope and one point p1 = (x1, y1) is given, then the equation can be written as,

`(y- y1)/(x-x1)` = m

If the line passes through the two points like P1 = (x1, y1) and P2 = (x2, y2), then the slope of the line can be written as

Slope m = `(y2- y1)/ (x2-x1)`

Example Problems on Equations of Straight Lines:
Line passes through the point (-1,3) and slope of the line is 2, find the equation of line.

Solution:

The slope of the line must be the same between any two points

Formula:

(y-y1)= m(x-x1)

Given:

x1=-1

y1=3   

Slope (m) =2

Then the equation of the line is given by:

y-3 =2 (x+1)

y=2(x+1) +3

y=2x+5   

Therefore the equation of straight line is y = 2x+5

Example: 2

Line passes through the point (4, 3), (5, 4), find the slope and equation of the straight line.

Solution:

Here x1=4

Y1=3

X2 =5

Y2=6

We know the formula for finding the slope m = (y2- y1)/ (x2-x1)

Substitute the above value in that equation,

m = (6-3)/(5-4)

=3/1

Therefore the slope of the line =3

Now we find the equation of the line,

Equation of line is (y-y1) = m(x-x1)

(y-3) =3(x-4)

(y-3) =3x-12

y=3x-12+3

y =3x-9

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