SAT Question 00b9bd37: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. A line in the xy-plane can be written as $y=mx+b$, where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept. The graph shown is a line passing through the points $(0,35)$ and $(90,0)$. Substituting $0$ for $x$ and $35$ for $y$ in the equation $y=mx+b$ yields $35=m(0)+b$, or $35=b$. Substituting $35$ for $b$, $90$ for $x$, and $0$ for $y$ in the equation $y=mx+b$ yields $0=90m+35$. Subtracting $35$ from both sides of this equation yields $-35=90m$. Dividing both sides of this equation by $90$ yields $-\frac{35}{90}=m$, or $-\frac{7}{18}=m$. Substituting $-\frac{7}{18}$ for $m$ and $35$ for $b$ in the equation $y=mx+b$ yields $y=-\frac{7}{18}x+35$. Multiplying both sides of this equation by $18$ yields $18y=-7x+35(18)$, or $18y=-7x+630$. Adding $7x$ to both sides of this equation yields $7x+18y=630$. Therefore, the equation $7x+18y=630$ represents the relationship between $x$ and $y$ modeled by the graph.