Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

What does the inequality 'y < 2x + 3' represent graphically?

Back

It represents the region below the line defined by the equation 'y = 2x + 3', not including the line itself.

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (like (0,0)). If it satisfies the inequality, shade the side containing that point; if not, shade the opposite side.

Front

What is the solution set of the inequality 'x ≥ -1'?

Back

The solution set includes all values of x that are greater than or equal to -1, represented graphically by a solid line at x = -1 and shading to the right.

Front

What does the inequality 'y ≥ -3' mean?

Back

It means that the value of y is greater than or equal to -3, represented graphically by a solid horizontal line at y = -3 and shading above.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert a linear equation to an inequality?

Back

To convert a linear equation to an inequality, replace the equal sign with an inequality symbol (>, <, ≥, ≤) based on the context of the problem.