Graphing Inequalities Practice Questions

The boundary line $x = -1$ is to be drawn on a grid.

Write down whether this line should be a solid line or a dashed line. Give a reason for your answer.

Show that the point $(1, 4)$ satisfies all three inequalities.

Write down the three inequalities that define the shaded region $R$.

On the grid below, show by shading, the region that satisfies all of these inequalities.

$$y \ge 0 \qquad x \le 3 \qquad y \le 2x + 2 \qquad x + y \le 5$$

Label the region $R$.

Find the four inequalities that define the shaded region.

For each point in the table, state whether or not it lies in region $R$.

Point	Does it lie in $R$?
$(1, 3)$
$(2, 2)$
$(4, 2)$
$(2, 3)$
$(0, 2)$

Write down the coordinates of a point that lies in region $R$ and has $y = 1$, where both coordinates are integers.

The boundary line $x + 2y = 8$ is drawn on a grid. Explain why this line must be drawn as a dashed line.

On the grid below, show by shading, the region $R$. Label the region $R$.

Work out the number of points with integer coordinates that lie in region $R$, including any points on its boundaries.