Which of the following statements is true about the graph of the inequality y≤ax+b, where a≠0?
The graph of the inequality is a solid line, and the shaded region is above the line.
The graph of the inequality is a dashed line, and the shaded region is below the line.
The graph of the inequality is a solid line, and the shaded region is below the line.
The graph of the inequality is a dashed line, and the shaded region is above the line.
Which of the following statements is true about the graph of the inequality y<ax+b, where a≠0?
please help me this is my last question
i just dont understand if it is a dotted or a solid line
To determine which statement is true about the graph of the inequality y ≤ ax + b, first let's understand the components involved.
The inequality y ≤ ax + b represents a linear inequality in two variables, where a≠0. This means that the graph of the inequality is a straight line in the coordinate plane.
Now, let's examine the possible options:
1. The graph of the inequality is a solid line, and the shaded region is above the line.
2. The graph of the inequality is a dashed line, and the shaded region is below the line.
3. The graph of the inequality is a solid line, and the shaded region is below the line.
4. The graph of the inequality is a dashed line, and the shaded region is above the line.
To determine which option is true, we need to consider the inequality symbol: "≤" (less than or equal to).
When the inequality includes the "≤" symbol, it implies that the shaded region includes the boundary line as well. This means that the boundary line should be a solid line, not dashed.
Additionally, the shaded region corresponds to the solutions that satisfy the inequality. As the inequality is y ≤ ax + b, we see that the shaded region is below the line, not above it. This eliminates option 1.
Therefore, the correct statement is:
The graph of the inequality is a solid line, and the shaded region is below the line.
To visualize this, you can plot the line y = ax + b and shade the region below it to represent the solutions that satisfy y ≤ ax + b.
= = solid
</= = solid
>/= = solid
< = dotted
> = dotted
solid means the points on the line are included
above is greater
below is less