Once you have the slope, use the point where $x=0$ to identify the $y$-intercept and write $y=mx+b$.

A dashed line means the boundary is not included, and a solid line means the boundary is included. Then use a test point like $(0,0)$ to decide whether the shading is above or below the line.

Enter $y=-\frac{3}{2}x+1$.

Evaluate a point like $(0,0)$. Since $0$ is less than $1$, the solution set should be the side of the line that contains $(0,0)$.

Because the boundary is solid, choose the inequality symbol that includes equality ($\le$ or $\ge$), not a strict symbol ($<$ or $>$).

Use the two points on the line, $(-2,4)$ and $(0,1)$.

The slope is

Since the line passes through $(0,1)$, the $y$-intercept is $1$, so the line is

The line is solid, so points on the line are included (use $\le$ or $\ge$).

A point like $(0,0)$ lies in the shaded region, and it is below the line because $0 \le 1$ when $x=0$.

So the shaded region represents points with $y$ less than or equal to the line.

Therefore, the inequality is $y \le -\frac{3}{2}x + 1$.