Understanding Systems of Inequalities

The video tutorial explains how to determine the system of inequalities that represents a shaded region on a graph. It covers finding the slope and y-intercept of lines, analyzing inequalities, and verifying points within the solution set. The tutorial also demonstrates how to graphically represent systems of inequalities and solve related problems.

What is the slope of a line if for every increase of 2 in x, y increases by 2?

• 3

• 2

• 1

• 0

If a line has a y-intercept of 1, what is the equation of the line with a slope of 1?

• y = 2x - 1

• y = x - 1

• y = 2x + 1

• y = x + 1

How do you determine if a shaded region is below a line on a graph?

• The line is dotted

• The region is below the line

• The line is solid

• The region is above the line

What inequality represents a shaded region below the line y = x + 1?

• y > x + 1

• y ≥ x + 1

• y < x + 1

• y ≤ x + 1

Which point satisfies the inequality 2y - x ≥ -6?

• (1, -1)

• (-4, 1)

• (3, 1)

• (0, 0)

What is the result of substituting x = 3 and y = 1 into the inequality 2y - 3x < -6?

• Both True and False

• Cannot be determined

• False

• True

What is the slope of a line if increasing x by 3 results in the same increase in y?

• 1

• 0

• 2

• 3

If a line has a y-intercept of -2 and a slope of 1, what is its equation?

• y = 2x + 2

• y = x + 2

• y = x - 2

• y = 2x - 2

What inequality represents a shaded region above the line y = -2x + 3?

• y ≥ -2x + 3

• y ≤ -2x + 3

• y > -2x + 3

• y < -2x + 3

How do you rearrange the inequality y - x ≤ -2 to have x and y on the same side?

• x + y ≥ 2

• x - y ≤ 2

• x - y ≥ 2

• x + y ≤ 2