Graphing Linear Inequalities and Systems

Front

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

Back

The slope-intercept form is 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

Are points on the boundary line included in the solution set of a linear inequality?

Back

Yes, points on the boundary line are part of the solution set if the inequality is 'greater than or equal to' or 'less than or equal to'.

Front

What does the inequality 20x + 30y > 1000 represent in a real-world context?

Back

It represents a scenario where Lee sold kitchen gadgets for $20 each (x) and home furnishings for $30 each (y), making over $1000.

Front

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

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality is represented by a shaded region on one side of the boundary line, which is either solid (inclusive) or dashed (exclusive).

Front

What does the inequality 3x - y > 4 mean in terms of y?

Back

It can be rewritten as y < 3x - 4.

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 set, while a dashed line indicates they are not.

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 as a dashed line and shade below the line.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more inequalities that are graphed on the same coordinate plane.