Extending Linear Relationships- Review

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does it mean when two lines are parallel in a linear system?

Back

When two lines are parallel, they have the same slope but different y-intercepts, meaning they will never intersect. Therefore, a linear system with parallel lines has no solution.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is y = |x|, which creates a V-shaped graph that opens upwards.

Front

How does the graph of y = |x + 2| - 5 transform from the parent function?

Back

The graph shifts left 2 units and down 5 units from the parent function y = |x|.

Front

What is the solution to the system of inequalities y ≥ -x - 1 and y ≥ x + 4?

Back

The solution is the region where both inequalities are satisfied, which includes points above the lines defined by the inequalities.

Front

What does it mean for a linear system to have infinitely many solutions?

Back

A linear system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it moves. A positive slope means the line rises, while a negative slope means it falls.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

Front

What is the effect of a negative coefficient in front of x in a linear equation?

Back

A negative coefficient in front of x indicates that the line will slope downwards from left to right.

Front

What does the term 'transformation' refer to in the context of functions?

Back

Transformation refers to changes made to the graph of a function, including shifts, stretches, compressions, and reflections.