Question

Given the linear inequality:

x + 2y < -25

Use the Line tool to graph the boundary of this inequality on the coordinate grid provided below. Once you've done that, use the Point tool to plot any point that is a solution to the inequality.

You should graph only ONE line and ONE point.

Answer 1

The graph of the boundary for the inequality
`\(x + 2y < -25\)` is a dashed line. A point that satisfies this inequality is plotted on the graph as well.

Explanation:

The linear inequality
`\(x + 2y < -25\)`represents a boundary line on the coordinate grid. To graph this, we first convert the inequality into a linear equation:
`\(x + 2y = -25\).` Since the inequality is
`\( < \)`(less than), the boundary line will be dashed to signify that the points on this line are not included in the solution set. Using the slope-intercept form, we rearrange the equation to solve for
`\(y\): \(y = -(1)/(2)x - (25)/(2)\).`With the slope
`(\(-(1)/(2)\))` and the y-intercept
`\(\left(0, -(25)/(2)\right)\)`, we plot the line on the grid.

For the point that satisfies the inequality, any point that lies below this dashed line would satisfy the condition. Let's consider a point like \((-5, -10)\) which clearly fits this criteria as when substituted into the inequality, it results in \((-5) + 2(-10) = -25\) (which is less than \(-25\)), confirming its validity as a solution.

In summary, the graph of the inequality
`\(x + 2y < -25\)`is depicted as a dashed line to indicate the boundary, while the point
`\((-5, -10)\)` (or any other point below this dashed line) serves as a valid solution to the inequality.