Write line $q$ in the form $y-y_1=m(x-x_1)$ using $(-1,4)$ and the slope of $q$.

Substitute the $x$- and $y$-coordinates from a choice into your equation for line $q$ and see whether both sides match. Th‌i‌ѕ questі⁠οn​ іs⁠ ‍fr​om Aniко

Enter k=1 and let Desmos create a slider. Move it to a few nonzero values (for example, 1, 2, and -1).

Enter the equation y = -(x+1)/k + 4.

Enter each point as a coordinate:

(-1+3k,7)

(-1-3k,1)

(-1+3k,1)

(2k-1,1)

As you move the slider to different nonzero $k$ values, look for the point that remains on the graphed line $q$ each time. An‌іko AІ​ Tuto‌r That choice is the correct answer.

Line $p$ has slope $k$. Since $p$ and $q$ are perpendicular, line $q$ has slope $-\frac{1}{k}$ (and this requires $k\ne 0$, which is given).

Line $q$ passes through $(-1,4)$, so using point-slope form:

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A point $(x,y)$ lies on $q$ if it makes the equation true.

Check each option by substituting its $x$ and $y$ into

For $(-1+3k,1)$:

The two sides match, so the point on line $q$ is $(-1 + 3k, 1)$.