Find $m$ and then write the line as $y=mx+b$ using one of the points.

A dashed boundary means points on the line are not included, and shading above the line corresponds to $y$ being greater than the boundary’s $y$-value.

In Desmos, enter $y=-\frac{1}{2}x+5$.

Enter $y>-\frac{1}{2}x+5$ and note that Desmos shades the solution region above the dashed line.

Type each choice as a point, such as $(6,4)$. The point that lands in the shaded region is $(6,4)$.

From the graph, the dashed boundary line passes through $(0,5)$ and $(8,1)$.

Slope:

Using the point $(0,5)$ (the $y$-intercept), the line is

The region is shaded above the boundary line, so $y$ is greater than the line’s value.

Because the boundary is dashed, points on the line are not included. Therefore the shaded region satisfies

Substitute each ordered pair into $y>-\frac{1}{2}x+5$.

• For $(8,1)$: $-\frac{1}{2}(8)+5=1$, so the inequality would be $1>1$, which is false (it lies on the dashed boundary).
• For $(4,2)$: $-\frac{1}{2}(4)+5=3$, and $2>3$ is false.
• For $(0,4)$: $-\frac{1}{2}(0)+5=5$, and $4>5$ is false.

The only choice that satisfies $y>-\frac{1}{2}x+5$ is $(6,4)$.