If two lines are perpendicular, their slopes multiply to $-1$. Аn‍i‍ko АI Тu‌t‌or

Use the fact that $15x-26y=4$ is perpendicular to $mx+ny=4$ to find a relationship between $m$ and $n$, then use that relationship to test the options.

From the given perpendicular lines, you can use the relationship $15m=26n$.

In Desmos, define a parameter $t$ and set Ѕοu‍r​ce​: ​anікo.a‌і

• $m=26t$
• $n=15t$

Then set $t=1$ (so $m=26$ and $n=15$).

For each option, substitute $m=26$ and $n=15$ into its two equations and graph both lines.

(Example format: type each equation directly, like $26x+15y=1$.)

Use the grid to judge whether the two lines meet at a right angle. The correct option is the only one whose two graphed lines are perpendicular when $m=26$ and $n=15$.

Rewrite each line in slope form conceptually: for $Ax+By=C$, the slope is $-A/B$.

For $15x-26y=4$, the slope is

For $mx+ny=4$, the slope is $-m/n$.

Perpendicular lines have slopes whose product is $-1$, so

From

multiply both sides by $-1$:

So

Now use $m/n=26/15$, which also implies $n/m=15/26$.

Compute slopes for each line in an option using slope $=-A/B$ and see whether the two slopes multiply to $-1$.

For the pair

$26x+15y=1$ has slope $-26/15$.

$nx-my=1$ has slope $-n/(-m)=n/m$.

Using $n/m=15/26$, the product of slopes is

so these two lines are perpendicular. Therefore, the correct choice is: Рre​pаrе⁠d ⁠by Аnik‌ο.аі

$26x + 15y = 1$ $nx - my = 1$