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

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

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05.01.2022

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

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

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

$y - y_{1} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x 1)$ ----- 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,

$y-0 = \frac{2-0}{6-0}(x-0)$

On simplifying above equation,

$y = \frac{2}{6} x=\frac{1}{3} x$

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

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