SAT Question 51568fb9: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. A linear equation can be written in the form $y=mx+b$, where $m$ is the slope of the graph of the equation in the xy-plane and $\left(0,b\right)$ is the y-intercept. Subtracting $10x$ from each side of the given equation, $10x-5y=-12$, yields $-5y=-10x-12$. Dividing each side of this equation by $-5$ yields $y=2x+\frac{12}{5}$. This equation is in the form $y=mx+b$, where $m=2$. Therefore, the slope of the graph of the given equation in the xy-plane is $2$.