The graph of "x + 5y < -5" is a dashed line with a slope of -1/5, passing through (0, -1). The shaded region below the line on the coordinate plane represents the solution set.
Graphing the linear inequality "x + 5y < -5" involves representing the set of points that satisfy this inequality on a coordinate plane. First, we rewrite the inequality in slope-intercept form (y = mx + b) to identify the slope and y-intercept. For "x + 5y < -5", we subtract x from both sides and then divide by 5, yielding "y < -1/5x - 1".
The slope (-1/5) indicates that the line slopes downward, and the y-intercept (-1) suggests it intersects the y-axis at (0, -1). Plot this point and use the slope to find another point, perhaps by moving one unit to the right and five units down.
Next, since the inequality is "y < -1/5x - 1", the line is dashed to represent that points on the line itself are not included in the solution. Shade the region below the line to depict all the points that satisfy the inequality. This shading indicates that any point in the shaded region, when substituted into the inequality, will make it true.
In summary, the graph of "x + 5y < -5" is a dashed line with a downward slope, passing through (0, -1), and the shaded region below the line represents the solution set.