SAT Question 0b46bad5: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. The given equation $ax+by=b$ can be rewritten in slope-intercept form, $y=mx+k$, where $m$ represents the slope of the line represented by the equation, and $k$ represents the $y$-coordinate of the $y$-intercept of the line. Subtracting $ax$ from both sides of the equation yields $by=-ax+b$, and dividing both sides of this equation by $b$ yields $y=-\frac{a}{b}x+\frac{b}{b}$, or $y=-\frac{a}{b}x+1$. With the equation now in slope-intercept form, it shows that $k=1$, which means the $y$-coordinate of the $y$-intercept is $1$. It's given that $a$ and $b$ are both greater than $0$ (positive) and that $a<b$. Since $m=-\frac{a}{b}$, the slope of the line must be a value between $-1$ and $0$. Choice C is the only graph of a line that has a $y$-value of the $y$-intercept that is $1$ and a slope that is between $-1$ and $0$.