The graph shows a linear inequality with shading below a line, which indicates the region where the inequality holds. Let's analyze the line’s slope and y-intercept to write the inequality in slope-intercept form.

Step-by-Step Solution:

1. Identify two points on the line: Looking at the line, two clear points are (0, -1) and (1, 0).
2. Calculate the slope (m): $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-1)}{1 - 0} = 1$ So, the slope $m = 1$.
3. Determine the y-intercept (b): The line crosses the y-axis at -1, so $b = -1$.

The equation of the line is: $y = x - 1$

4. Determine the inequality symbol: Since the shaded region is below the line, we use $\leq$ (for “less than or equal to”) to include the boundary line.

Final Answer:

The inequality is: $y \leq x - 1$

Would you like further details or have any questions?

Related Questions:

1. How do you determine if the inequality is $\leq$ or $\geq$ based on the shading?
2. What changes if the shaded region was above the line?
3. How would you solve for $x$ if given an inequality in slope-intercept form?
4. What are the differences between linear inequalities and linear equations?
5. How would you graph $y > x - 1$ on a coordinate plane?

Tip: Always verify if the shaded region includes the boundary line by checking if the line is solid (for $\leq$ or $\geq$) or dashed (for $<$ or $>$).