SAT Question 9aaf7786: Linear Equations In Two Variables answer and explanation with Desmos solution

A line in the xy-plane can be represented by the equation $y=mx+b$, where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept. It's given that line $p$ has a slope of $-\frac{5}{3}$. Therefore, $m=-\frac{5}{3}$. It's also given that line $p$ has an x-intercept of $\left(-6,0\right)$. Therefore, when $x=-6$, $y=0$. Substituting $-\frac{5}{3}$ for $m$, $-6$ for $x$, and $0$ for $y$ in the equation $y=mx+b$ yields $0=\left(-\frac{5}{3}\right)\left(-6\right)+b$, which is equivalent to $0=10+b$. Subtracting $10$ from both sides of this equation yields $-10=b$. Therefore, the y-coordinate of the y-intercept of line $p$ is $-10$.