Max is giving the graph of a linear inequality 3x - 7.2 y is less than 0 and after determine whether a given point is a solution she notices that the point falls on the boundary line of the draft what should she conclude

1 answer

When determining whether a point is a solution to a linear inequality, it's essential to consider the nature of the inequality.

The inequality \(3x - 7.2y < 0\) has a corresponding boundary line, which can be found by setting the inequality to equality:

\[3x - 7.2y = 0.\]

This boundary line can be expressed as \(y = \frac{3}{7.2}x\).

Now, regarding the point that Max is checking, if it falls on the boundary line, it means that when you substitute the coordinates of that point into the equation of the boundary line, the equation holds true (i.e., the equation equal to zero).

Since the original inequality is a "less than" inequality (i.e., \(<\)), any point on the boundary line itself does not satisfy the inequality. Therefore, Max should conclude that if the point is on the boundary line given by \(3x - 7.2y = 0\), the point is not a solution to the inequality \(3x - 7.2y < 0\).

In summary, for a point to be a solution to the inequality \(3x - 7.2y < 0\), it must fall in the region that satisfies the inequality, which is below the boundary line (if we consider a graph with standard orientation where the y-axis is vertical).