Answer :
To determine which statement about a linear inequality is true, let's analyze each statement individually:
1. It will intersect at a 90-degree angle:
This statement doesn't make sense in the context of a linear inequality. Linear inequalities represent half-planes and their boundaries (lines), so intersection at a specific angle isn’t a characteristic of linear inequalities in general.
2. The algebraic representation will contain an inequality rather than an equal sign:
This is a correct statement. Linear inequalities are written in the form of [tex]\(ax + by < c\)[/tex], [tex]\(ax + by \leq c\)[/tex], [tex]\(ax + by > c\)[/tex], or [tex]\(ax + by \geq c\)[/tex], utilizing inequality symbols rather than the equal sign used in linear equations.
3. It will contain parallel or perpendicular lines:
While linear inequalities might represent regions bounded by lines that can be parallel or perpendicular, this is not a definitive characteristic of linear inequalities themselves but rather a specific geometric scenario that can occur within linear systems.
4. Two of these are true:
This can only be true if two of the statements above are correct. However, we have identified only one correct statement regarding the algebraic representation containing an inequality sign rather than an equal sign.
After the analysis, the correct statement regarding a linear inequality is:
The algebraic representation will contain an inequality rather than an equal sign.
1. It will intersect at a 90-degree angle:
This statement doesn't make sense in the context of a linear inequality. Linear inequalities represent half-planes and their boundaries (lines), so intersection at a specific angle isn’t a characteristic of linear inequalities in general.
2. The algebraic representation will contain an inequality rather than an equal sign:
This is a correct statement. Linear inequalities are written in the form of [tex]\(ax + by < c\)[/tex], [tex]\(ax + by \leq c\)[/tex], [tex]\(ax + by > c\)[/tex], or [tex]\(ax + by \geq c\)[/tex], utilizing inequality symbols rather than the equal sign used in linear equations.
3. It will contain parallel or perpendicular lines:
While linear inequalities might represent regions bounded by lines that can be parallel or perpendicular, this is not a definitive characteristic of linear inequalities themselves but rather a specific geometric scenario that can occur within linear systems.
4. Two of these are true:
This can only be true if two of the statements above are correct. However, we have identified only one correct statement regarding the algebraic representation containing an inequality sign rather than an equal sign.
After the analysis, the correct statement regarding a linear inequality is:
The algebraic representation will contain an inequality rather than an equal sign.
