Graphing Systems of Linear Inequalities in Two Variables

The video tutorial explains how to graph and shade regions for systems of linear equations. It covers multiple examples, demonstrating how to handle inequalities and standard form equations. The tutorial emphasizes finding the correct region where all conditions are satisfied by shading the appropriate areas on the graph.

What type of line is represented by x > -1?

• Curved line

• Diagonal line

• Vertical line

• Horizontal line

In the first example, which region should be shaded for y < 2?

• To the right of the vertical line

• Below the horizontal line

• Above the horizontal line

• To the left of the vertical line

For the equation y > 2x - 3, what is the slope?

• 2x

• -3

• 3

• 2

In the second example, which region is shaded for y < -x + 5?

• Above the gray line

• Below the gray line

• To the left of the gray line

• To the right of the gray line

For the equation x > 1, which side of the line should be shaded?

• Below

• Left

• Right

• Above

In the third example, which region is shaded for y > 3/2x - 3?

• Above the blue line

• To the right of the blue line

• Below the blue line

• To the left of the blue line

What is the first step in solving 2x + 3y > 6 for y?

• Multiply by 3

• Add 2x to both sides

• Subtract 2x from both sides

• Divide by 3

In the fourth example, what is the slope of the line 3x - 4y ≤ 12?

• -4/3

• 4/3

• -3/4

• 3/4

For the equation y ≥ 3/4x - 3, which region should be shaded?

• Below the line

• To the right of the line

• Above the line

• To the left of the line

In the final example, what is the y-intercept of the line y ≥ 3/4x - 3?

• -4

• -3

• 4

• 3