Answer:
Equation of the line passing through points (6, 2) , (0, 0) is [tex]\bold{y = \frac{1}{3} x}[/tex]
Solution:
Equation of line passing through two points [tex]A(x 1, y 1) \text { and } B(x 2, y2)[/tex] is given as,
[tex]y - y1 = m(x - x1)[/tex] --- eqn 1
Where m is slope of line AB and value of m is given as
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
By substituting the value of “m” in eqn 1, we get
[tex]y - y_{1} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x 1)[/tex] ----- eqn 2
From question, given that two points are (6, 2), (0, 0).
Hence we get [tex]x_{1}=6 ; x_{2}=0 ; y_{1}=2 ; y_{2}=0[/tex]
By substituting the values in eqn 2,
[tex]y-0 = \frac{2-0}{6-0}(x-0)[/tex]
On simplifying above equation,
[tex]y = \frac{2}{6} x=\frac{1}{3} x[/tex]
Hence equation of the line having points (6, 2) and (0, 0) is [tex]\bold{y=\frac{1}{3}x}[/tex]
