Question 610·Hard·Math

At an intersection, the line and the graph have the same $x$ and $y$, so line $t$ passes through $(-1,f(-1))$ and $(2,f(2))$. The line's slope needs both function outputs, even though the function itself isn't a line.

Type $f(x)=2^x+x$, then $f(-1)$ in Desmos. It shows $-0.5=-\frac12$, so the first point is $(-1,-\frac12)$. The negative exponent gives $2^{-1}=\frac12$; the separate $+x$ adds $-1$. Don't make the exponent's minus sign a minus sign on the fraction.

On the next line, type $f(2)$. Desmos shows $6$, so the second point is $(2,6)$.

The slope is the change in $y$ divided by the change in $x$. Take the second point minus the first in both places:

Type $\frac{f(2)-f(-1)}{2-(-1)}$ in Desmos. It gives $\frac{13}{6}$ (use the fraction button if it displays a decimal). So the slope of line $t$ is $\frac{13}{6}$. Choice D.