SAT Question 9bbce683: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. The equation of line $h$ can be written in slope-intercept form $y=mx+b$, where $m$ is the slope of the line and $\left(0,b\right)$ is the y-intercept of the line. It's given that line $h$ contains the points $\left(18,130\right)$, $\left(23,160\right)$, and $\left(26,178\right)$. Therefore, its slope $m$ can be found as $\frac{160-130}{23-18}$, or $6$. Substituting $6$ for $m$ in the equation $y=mx+b$ yields $y=6x+b$. Substituting $130$ for $y$ and $18$ for $x$ in this equation yields $130=6(18)+b$, or $130=108+b$. Subtracting $108$ from both sides of this equation yields $22=b$. Substituting $22$ for $b$ in $y=6x+b$ yields $y=6x+22$. Since line $k$ is the result of translating line $h$ down $5$ units, an equation of line $k$ is $y=6x+22-5$, or $y=6x+17$. Substituting $0$ for $y$ in this equation yields $0=6x+17$. Solving this equation for $x$ yields $x=-\frac{17}{6}$. Therefore, the x-intercept of line $k$ is $\left(-\frac{17}{6},0\right)$.