Parallel lines in the coordinate plane always have the same slope. Once you know the slope of the given line, you also know the slope of line $k$.

Use the slope you found and the point $(2,-1)$ in either point-slope form $y - y_1 = m(x - x_1)$ or slope-intercept form $y = mx + b$ to find the new line's equation.

Once you have line $k$ in the form $y = mx + b$, the $y$-intercept is the constant term $b$. Focus on that value.

In Desmos, enter 4x-3y=12. Then, in a new line, enter y=(4/3)x-4. You should see that this second equation lies exactly on top of the first, confirming the slope is $\tfrac{4}{3}$.

In another expression line, type y=(4/3)x+b. Desmos will create a slider for b; this represents all lines parallel to the original one.

Add the point (2,-1) as a new expression so you can see it on the graph. Then adjust the b slider until the line y=(4/3)x+b passes exactly through the point (2,-1).

Once the line goes through (2,-1), look at the current value of b in y=(4/3)x+b. That value of b is the $y$-intercept of line $k$.

Rewrite the equation $4x - 3y = 12$ in slope-intercept form $y = mx + b$:

Subtract $4x$ from both sides:

Divide every term by $-3$:

So the slope of the given line is $m = \tfrac{4}{3}$.

Line $k$ is parallel to the given line, so it has the same slope $m = \tfrac{4}{3}$.

Line $k$ passes through $(2,-1)$, so use the point-slope form $y - y_1 = m(x - x_1)$:

which simplifies the left side to

Distribute on the right-hand side:

So the equation is

Subtract 1 from both sides:

Write $1$ as $\tfrac{3}{3}$ to combine fractions:

In slope-intercept form $y = mx + b$, the $y$-intercept is $b$, so the $y$-intercept of line $k$ is $-\frac{11}{3}$.