Question

Find the equations of the line joining the points
A (1, 1) and B (2,3)​

Answer 1

Answer:

x - 2y + 1 = 0

Step-by-step explanation:

two point slope form

y-y1 = (y2 - y1 )/(x2-x1) × x - x1

y - 1 = 2-1 / 3-1 × (×-1)

y-1 = 1/ 2 ×( x-1)

2y - 2 = x -1

× - 2y +1 =0

Answer 2

Answer:

The equation for line joining two points

(

x

1

,

y

1

)

and

(

x

2

,

y

2

)

is given by

y

−

y

1

y

2

−

y

1

=

x

−

x

1

x

2

−

x

1

and for given points it is

y

=

1

3

x

+

11

3

Explanation:

Let the slope intercept form of equation be

y

=

m

x

+

c

here we do not know the slope

m

and

y

-intercept

c

What we know is that this passes through the two coordinate pairs, say

(

x

1

,

y

1

)

and

(

x

2

,

y

2

)

.

As such we have three equations

y

=

m

x

+

c

......(1)

y

1

=

m

x

1

+

c

......(2) and

y

2

=

m

x

2

+

c

......(3)

Now using these let us eliminate

m

and

c

subtracting (2) from (1), we get

(

y

−

y

1

)

=

m

(

x

−

x

1

)

......(4)

and subtracting (2) from (3), we get

(

y

−

2

−

y

1

)

=

m

(

x

2

−

x

1

)

......(5