Linear Functions & Inequalities

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you determine if a point lies on a linear function?

Back

To determine if a point (x, y) lies on a linear function, substitute the x-value into the function's equation and see if the resulting y-value matches the y-value of the point.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

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 sign.

Front

What is a test point in the context of inequalities?

Back

A test point is a specific point used to determine which side of the line to shade when graphing an inequality.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is not included, while 'greater than or equal to' (≥) means the value is included in the solution set.