# Find the cartesian equation of the line which passes through the point $\left ( -2,4,-5 \right )$ and is parallel to the line  $\frac{x+3}{3}= \frac{4-y}{5}= \frac{z+8}{6}$

Given: hence $\frac{x+3}{3}= \frac{4-y}{5}= \frac{z+8}{6}$  passing through point $\left ( -2,4,-5 \right )$
As there 2 lines are parallel, their direction ratios will be equal ratios
Equation of the given line is
$\frac{x+3}{3}= \frac{4-y}{5}= \frac{z+8}{6}$
$\Rightarrow \frac{x+2}{3}= \frac{y-4}{-5}= \frac{z+5}{6}$
or $\Rightarrow \frac{x+2}{3}= \frac{4-y}{5}= \frac{z+5}{6}$  which is the required equation.

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