SAT Question c4ea43ef: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. Avery earns $$10$ per hour working at job A. Therefore, if she works $a$ hours at job A, she will earn $$10a$ dollars. Avery earns $$20$ per hour working at job B. Therefore, if she works $b$ hours at job B, she will earn $$20b$ dollars. The graph shown represents all possible combinations of the number of hours Avery could have worked at the two jobs to earn $s$ dollars. Therefore, if she worked $a$ hours at job A, worked $b$ hours at job B, and earned $s$ dollars from both jobs, the following equation represents the graph: $10a+20b=s$, where $s$ is a constant. Identifying any point $(a,b)$ from the graph and substituting the values of the coordinates for $a$ and $b$, respectively, in this equation yield the value of $s$. For example, the point $(16,0)$, where $a=16$ and $b=0$, lies on the graph. Substituting $16$ for $a$ and $0$ for $b$ in the equation $10a+20b=s$ yields $10\times 16+20\times 0=s$, or $160=s$. Similarly, the point $(0,8)$, where $a=0$ and $b=8$, lies on the graph. Substituting $0$ for $a$ and $8$ for $b$ in the equation $10a+20b=s$ yields $10\times 0+20\times 8=s$, or $160=s$.