Question

What is the equation of the following line written in general form?

y - x + 1 = 0
x - y + 1 = 0
-x - y + 1 = 0

Answer 1

eq. of line through (1,2) and (4,5) is

`y-y1= (y2-y1)/(x2-x1) (x-x1), y-2= (5-2)/(4-1) (x-1)`
`y-2= (3)/(3) (x-1) y-2=x-1 y-2-x+1=0 y-x-1=0`
x-y+1=0

Answer 2

`x-y+1=0`

Explanation:

To find the equation of the line , use the points from the graph of the line

(1,2) and (4,5)

First frame equation of the line
`y=mx+b`

`slope (m)=(y_2-y_1)/(x_2-x_1) =(5-2)/(4-1) =1`

m=1, (1,2)

`y=mx+b`

`2=1(1)+b`

b=1

So equation of the line is

`y=1x+1`

General form is Ax+By+C=0

Subtract 1x from both sides

`y=1x+1`

`-1x+y=1`, subtract 1 from both sides

`-1x+y-1=0`

Divide whole equation by -1

`x-y+1=0`