To graph the inequality $y < 1 - 3x$, we need to follow these steps:

1. Convert the inequality to slope-intercept form: The inequality $y < 1 - 3x$ is already in slope-intercept form, $y < mx + b$, where $m = -3$ (slope) and $b = 1$ (y-intercept).

2. Graph the boundary line: The boundary is $y = 1 - 3x$. Since the inequality is strictly less than ($<$), we use a dashed line for the graph. This line passes through:

   • $(0, 1)$, where $x = 0$ (the y-intercept), and
   • $(1, -2)$, since $y = 1 - 3(1) = -2$.

3. Shade the solution region:

   • The inequality $y < 1 - 3x$ means we shade below the dashed line.

4. Choose the correct graph: By analyzing the graphs provided:

   • The correct graph is bottom right, where the line is dashed, and the region below the line is shaded.

Do you want a detailed explanation of any of these steps or more help with similar questions?

Related Questions

1. What is the significance of the dashed vs. solid lines in inequality graphs?
2. How do you determine the region to shade for $y >$ or $y <$ inequalities?
3. What if the inequality was $y \leq 1 - 3x$? How would the graph change?
4. Can inequalities ever result in vertical or horizontal lines? If so, how?
5. How can you verify your solution for inequalities graphically?

Tip: Always test a point (like $(0, 0)$) to confirm which side of the line to shade!