Parallel lines have the same slope. Once you know the slope of line $k$, use that same slope for line $m$.

After you write line $m$ as $y = mx + b$ with the correct slope, plug in $x = 6$ and $y = -5$ to find $b$.

Once you find the full equation of line $m$, compare it to the answer choices and also make sure it passes through $(6,-5)$.

Type 4y - 8x = 12 into Desmos. Then, if needed, click the graph or rewrite it as y = 2x + 3 so you can recognize that the slope of line $k$ is $2$.

Enter each option into Desmos as separate equations: y = -2x - 17, y = 2x + 17, y = -2x + 17, and y = 2x - 17. Visually compare their steepness and direction to line $k$ to see which have the same slope (are parallel).

Plot the point (6, -5) in Desmos. Then look at which of the lines that are parallel to line $k$ also pass exactly through the point (6, -5). The line that is both parallel and passes through the point is the correct answer.

Start with the equation of line $k$:

Solve for $y$ to put it in slope-intercept form $y = mx + b$:

Divide every term by $4$:

So line $k$ has slope $m = 2$.

Parallel lines have equal slopes.

Since line $k$ has slope $2$, line $m$ must also have slope $2$.

So line $m$ has the form

for some $b$ (the $y$-intercept) that we still need to find.

We know line $m$ passes through $(6, -5)$, so its equation $y = 2x + b$ must be true when $x = 6$ and $y = -5$.

Substitute $x = 6$ and $y = -5$ into $y = 2x + b$:

-5 = 12 + b

From the equation

subtract $12$ from both sides:

b = -17

y = 2x - 17