Question

What is the equation of the following line (6,2) (0,0)

Answer 1

m=2/6=1/3

y-0=1/3(x-0)
y=x/3
Or y=(1/3)(x)

Answer 2

Equation of the line passing through points (6, 2) , (0, 0) is
`\bold{y = (1)/(3) x}`

Solution:

Equation of line passing through two points
`A(x 1, y 1) \text { and } B(x 2, y2)` is given as,

`y - y1 = m(x - x1)` --- eqn 1

Where m is slope of line AB and value of m is given as

`m = (y_(2)-y_(1))/(x_(2)-x_(1))`

By substituting the value of “m” in eqn 1, we get

`y - y_(1) = (y_(2)-y_(1))/(x_(2)-x_(1))(x-x 1)` ----- eqn 2

From question, given that two points are (6, 2), (0, 0).

Hence we get
`x_(1)=6 ; x_(2)=0 ; y_(1)=2 ; y_(2)=0`

By substituting the values in eqn 2,

`y-0 = (2-0)/(6-0)(x-0)`

On simplifying above equation,

`y = (2)/(6) x=(1)/(3) x`

Hence equation of the line having points (6, 2) and (0, 0) is
`\bold{y=(1)/(3)x}`