Jika garis 2x−7y+5=0 direfleksi terhadap sumbu y dan dilanjutkan translasi T= -8 4 , maka bayangan garis tersebut adalah …. 2x−7y+17=0 2x−7y−17=0 7x+2y+17=0 2x+7y−17=0 2x−7y−17=0

When a point $(x,y)$ is reflected across the y-axis, its new coordinates $(x',y')$ are given by $x' = -x$ and $y' = y$.
From these relations, we can express $x$ and $y$ in terms of $x'$ and $y'$:
$x = -x'$
$y = y'$
Substitute these into the original line equation:

$$2(-x') - 7(y') + 5 = 0$$ $$-2x' - 7y' + 5 = 0$$

Multiply by -1 to get a positive coefficient for $x$:

$$2x' + 7y' - 5 = 0$$

So, the equation of the line after reflection is $2x + 7y - 5 = 0$.

When a point $(x',y')$ is translated by $T = \begin{pmatrix} a \\ b \end{pmatrix}$, its new coordinates $(x'',y'')$ are given by $x'' = x' + a$ and $y'' = y' + b$.
Here, $a = -8$ and $b = 4$.
So, $x'' = x' - 8 \implies x' = x'' + 8$
And $y'' = y' + 4 \implies y' = y'' - 4$
Substitute these into the equation of the reflected line:

$$2(x'' + 8) + 7(y'' - 4) - 5 = 0$$ $$2x'' + 16 + 7y'' - 28 - 5 = 0$$ $$2x'' + 7y'' + (16 - 28 - 5) = 0$$ $$2x'' + 7y'' - 17 = 0$$

The final equation of the line after translation is $2x + 7y - 17 = 0$.

The correct option is 2x+7y-17=0.