Linear Inequalities

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 identify the slope and y-intercept from the equation y = -x + 4?

Back

The slope (m) is -1 and the y-intercept (b) is 4.

Front

What does the inequality -y < x - 8 represent when solved for y?

Back

When solved for y, the inequality becomes y > -x + 8.

Front

What is the graphical representation of the inequality 5x + y ≤ -1?

Back

The graph includes the line 5x + y = -1 and the area below this line, including the line itself.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the coordinate plane that satisfies the inequality.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality.

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.