Once you know the slope $m$, plug it into $y=mx+b$ and then substitute the coordinates of one of the points to solve for $b$.

After you find an equation, plug in both $(2,3)$ and $(6,1)$ to make sure they satisfy it. Then match your equation to one of the answer choices.

In Desmos, type (2,3) on one line and (6,1) on the next line. Desmos will plot these as two points on the coordinate plane.

On new lines, enter each option exactly: y=2x-1, y=-1/2x+4, y=-2x+7, and y=1/2x+2. You will see four different lines.

Look at which one of the four lines goes through both plotted points $(2,3)$ and $(6,1)$. The equation of that line is the correct answer choice.

Use the slope formula with points $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(6,1)$:

So the slope $m$ of the line is $-\tfrac12$.

The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.

We already found $m=-\tfrac12$, so the equation becomes

Now we just need to find $b$.

Use either point; take $(2,3)$. Substitute $x=2$ and $y=3$ into $y=-\tfrac12 x + b$:

Compute $-\tfrac12\cdot 2$ to simplify and then solve for $b$.

From the previous step:

Add $1$ to both sides:

So the equation of the line is

which matches choice B.