Question 358·Hard·Algebra

The slope is the change in $y$ divided by the change in $x$. Take the points in the same order in both changes. Type $\frac{3-8}{1-(-5)}$ in Desmos; it shows $-0.833333\ldots$. Tap its fraction button to see $-\frac{5}{6}$. So $y$ drops by $5$ whenever $x$ increases by $6$.

At an $x$-intercept, $y=0$, not $x=0$. From $(1,3)$ to $(k,0)$, the change in $y$ is $0-3$, and the change in $x$ is $k-1$. The line keeps the slope you found, so change in $y$ equals slope times change in $x$:

In Desmos, replace $k$ with $x_1$ and $=$ with $\sim$ so it solves for the unknown coordinate. Type $0-3\sim-\frac{5}{6}(x_1-1)$. Under PARAMETERS, Desmos shows $x_1=4.6$. Type $x_1$ on the next line and tap its fraction button to see $\frac{23}{5}$. The line crosses the $x$-axis at $\left(\frac{23}{5},0\right)$, so $k=\frac{23}{5}$. Choice C.