Question

if the distance between the lines y =mx and y=mx+6√5units then the value of m is​

Answer 1

The value of $m$ is $2.45$

Step-by-step explanation:

Given,

The two lines $y=mx$ and $y=mx+6$ and the distance between this two line $\sqrt{5}\ units$

For the line $y=mx+c_{1}\ and\ y=mx+c_{2}$

Distance is given,

$d=\frac{\left | c_{1}-c_{2} \right |}{\sqrt{1+m^{2} } }$__1

From the line,

$y=mx$ and $y=mx+6$

$c_{1}=0$ and $c_{2}=6$

From equation-1,

$\frac{\left | 0-6 \right |}{\sqrt{1+m^{2} } }=\sqrt{5}$

⇒$6=\sqrt{5}\times\sqrt{1+m^{2} }$

By squaring on both sides,

⇒$36=5(1+m^{2})$

⇒$1+m^{2}=\frac{36}{5}$

⇒$m^{2}=\frac{36}{5}-1$

⇒$m=\sqrt{\frac{31}{5} }$

⇒$m=2.45$

So, The value of $m$ is $2.45$