Graphing Inequalities and Test Points

The video tutorial explains how to solve systems of inequalities by following a structured game plan. It involves graphing the equations as if they were equalities, determining whether the lines are dashed or solid, and testing points to decide the shading direction. The tutorial demonstrates these steps with two inequalities, showing how to graph them, test points, and shade the appropriate regions to find the solution set.

What is the first step in solving systems of inequalities?

• Test a point

• Determine the type of line

• Graph the inequalities as equations

• Shade the region

When graphing the first inequality, what is the equation used?

• 3x + 2y = 6

• 2x - 7y = 14

• 3x + 2y < 6

• 2x - 7y ≥ 14

How do you determine the x-intercept for the first inequality?

• Set x to 0 and solve for y

• Use the slope-intercept form

• Use the midpoint formula

• Set y to 0 and solve for x

What type of line is used for the inequality 3x + 2y < 6?

• Dashed line

• Dotted line

• Bold line

• Solid line

Which point is commonly used to test the shading direction?

• (1, 1)

• (0, 0)

• (2, 2)

• (3, 3)

What is the result of testing the point (0, 0) in the inequality 3x + 2y < 6?

• True, shade towards the point

• False, shade away from the point

• False, shade towards the point

• True, shade away from the point

What is the equation used for graphing the second inequality?

• 2x - 7y = 14

• 2x - 7y ≥ 14

• 3x + 2y = 6

• 3x + 2y < 6

How do you determine the y-intercept for the second inequality?

• Use the slope-intercept form

• Use the midpoint formula

• Set x to 0 and solve for y

• Set y to 0 and solve for x

What type of line is used for the inequality 2x - 7y ≥ 14?

• Solid line

• Dashed line

• Dotted line

• Bold line

What is the result of testing the point (0, 0) in the inequality 2x - 7y ≥ 14?

• False, shade away from the point

• True, shade towards the point

• True, shade away from the point

• False, shade towards the point