Graphing Systems of Inequalities

The video tutorial explains how to solve systems of inequalities by graphing. It covers converting inequalities to equations, identifying slopes and intercepts, and graphing using dashed lines. The tutorial also demonstrates how to determine shading regions using test points, specifically the origin, to identify true and false regions. The video concludes with a summary of the steps involved in graphing systems of linear inequalities.

What is the first step in solving systems of inequalities by graphing?

• Convert inequalities to equations

• Plot the x-intercept

• Identify the solution region

• Shade the graph

What form should inequalities be in to easily identify the slope and y-intercept?

• Slope-intercept form

• Standard form

• Point-slope form

• Quadratic form

How should the slope be written for graphing purposes?

• As a decimal

• As a percentage

• As a fraction

• As a whole number

What is the significance of the y-intercept in graphing?

• It is the lowest point on the graph

• It is the highest point on the graph

• It is where the line crosses the y-axis

• It determines the slope

What does the slope of 1 over 1 indicate about the line?

• It falls one unit for every unit it runs

• It rises one unit for every unit it runs

• It is a vertical line

• It is a horizontal line

What is the significance of the slope in graphing?

• It determines the y-intercept

• It shows the steepness and direction of the line

• It is the highest point on the graph

• It is the lowest point on the graph

What does the y-intercept represent in a graph?

• The lowest point on the graph

• The point where the line crosses the x-axis

• The point where the line crosses the y-axis

• The highest point on the graph

Why are dashed lines used when graphing certain inequalities?

• To show that the boundary is not part of the solution

• To indicate a solid boundary

• To make the graph more visible

• To highlight the solution region

How can you represent a positive slope using negative numbers?

• By using positive numbers in both numerator and denominator

• By using a negative denominator only

• By using a negative numerator only

• By using negative numbers in both numerator and denominator

What is the y-intercept of the first inequality in the example?

• 1

• 3

• -1

• 0