When two lines are parallel, how are their slopes related? Use that relationship to write a general equation for line $m$ with an unknown intercept $b$.

Substitute the coordinates of the point $(3,2)$ into your general equation for line $m$ to solve for $b$.

Once you find the full equation of line $m$, compare it to the options and also double-check that your choice has the correct slope and passes through $(3,2)$.

In Desmos, enter y = -2x + 5 to see the reference line and its slope visually.

Type (3,2) into Desmos to plot the point that must lie on line m.

One by one, enter the equations y = 2x + 8, y = -2x - 8, y = -1/2x + 8, and y = -2x + 8. Observe which of these lines is parallel to y = -2x + 5 (same steepness and direction) and also passes exactly through the point (3,2).

The correct answer choice is the one whose graph is parallel to y = -2x + 5 and goes through the plotted point (3,2).

The given line is $y = -2x + 5$, which is in slope-intercept form $y = mx + b$.

So the slope $m$ of this line is $-2$.

Parallel lines in the $xy$-plane always have the same slope.

Since line $m$ is parallel to $y = -2x + 5$, line $m$ must also have slope $-2$.

So line $m$ has the form $y = -2x + b$ for some $y$-intercept $b$ that we still need to find.

We are told that line $m$ passes through the point $(3,2)$.

Any point on a line must satisfy its equation, so plug $x = 3$ and $y = 2$ into $y = -2x + b$:

Now solve this equation for $b$.

Continue solving:

So the equation of line $m$ is $y = -2x + 8$, which matches answer choice D.