SAT Question 6d8ad460: Linear Equations In Two Variables answer and explanation with Desmos solution

It’s given that line $j$ is perpendicular to line $k$ in the xy-plane. This means that the slope of line $j$ is the opposite reciprocal of the slope of line $k$. For a line that passes through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ in the xy-plane, the slope of the line can be calculated as $\frac{y_2-y_1}{x_2-x_1}$. It's shown that line $k$ passes through the points $(-6,0)$ and $(0,-5)$ in the xy-plane. Substituting $-6$ for $x_1$, $0$ for $y_1$, $0$ for $x_2$, and $-5$ for $y_2$ in $\frac{y_2-y_1}{x_2-x_1}$ yields $\frac{-5-0}{0-(-6)}$, or $-\frac{5}{6}$. The opposite reciprocal of $-\frac{5}{6}$ is $\frac{6}{5}$. Therefore, the slope of line $j$ is $\frac{6}{5}$. Note that 6/5, 1.2, and 1.20 are examples of ways to enter a correct answer.