CLASSWORK 6.5 DAY-2

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph the inequality y ≥ x - 3?

Back

To graph y ≥ x - 3, first graph the line y = x - 3 as a solid line (since it includes equality). Then shade the region above the line.

Front

What does it mean when a graph is shaded 'above' a line?

Back

Shading 'above' a line indicates that the solutions to the inequality are all the points where the y-values are greater than the y-values on the line.

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' or 'less than or equal to'.

Front

What does the inequality y < -3 represent on a graph?

Back

The inequality y < -3 represents all the points below the horizontal line y = -3, not including the line itself.

Front

How do you determine the correct inequalities from a graph of two lines?

Back

To determine the correct inequalities, observe the shaded regions and the position of the lines. Identify whether the lines are solid or dashed and whether the shading is above or below.

Front

What does the inequality x > 2 indicate on a graph?

Back

The inequality x > 2 indicates all the points to the right of the vertical line x = 2, not including the line itself.

Front

What is the difference between y ≥ -x - 1 and y < -x - 1?

Back

y ≥ -x - 1 includes the line (solid line) and the area above it, while y < -x - 1 does not include the line (dashed line) and includes the area below it.

Front

How do you solve a system of inequalities graphically?

Back

To solve a system of inequalities graphically, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What does the inequality y > -x - 1 represent?

Back

The inequality y > -x - 1 represents all the points above the line y = -x - 1, not including the line itself.