Question

Max is given the graph of the linear inequality 3x -7.2y <0 and asked to determine whether a given point is a solution.

Answer 1

To determine whether a given point is a solution to the linear inequality \(3x - 7.2y < 0\), you need to substitute the coordinates of that point into the inequality.

Here's how you can do it step by step:

1. **Identify the Point**: Let's say the given point is \((x_0, y_0)\).

2. **Substitute into the Inequality**: Replace \(x\) with \(x_0\) and \(y\) with \(y_0\) in the inequality:

\[
3x_0 - 7.2y_0 < 0
\]

3. **Evaluate the Expression**: Calculate the left-hand side \(3x_0 - 7.2y_0\).

4. **Determine the Result**:
- If the result is less than 0, then the point \((x_0, y_0)\) is a solution to the inequality.
- If the result is greater than or equal to 0, then the point is not a solution.

For example, if the point is \( (2, 1) \):
1. Substitute into the inequality:
\[
3(2) - 7.2(1) < 0
\]
\[
6 - 7.2 < 0
\]
\[
-1.2 < 0 \quad \text{(True)}
\]

Thus, the point \((2, 1)\) is a solution to the inequality \(3x - 7.2y < 0\).

If you have a specific point in mind, please provide it and I can help you evaluate it!