Question

Graph the linear inequality by shading the points not satisfying it. (for questions 4 \& 5) 4) x≤2y 5) 3x−2y≥12

Answer 1

4) The graph for x≤2y represents a shaded area above the line y ≥ 1/2x.This shaded area will represent all the points that does not satisfy the inequality

5) The graph for 3x−2y≥12 represents a shaded area below the line y ≤ (3/2)x - 6. This shaded area will represent all the points that does not satisfy the inequality

Step-by-step explanation:

4. x ≤ 2y

To graph the inequality x ≤ 2y, we'll first rearrange the equation:

y ≥ 1/2x

To plot this line, select a few x values and calculate corresponding y values to create points for plotting.

Let's choose (x = 0) and (x = 5) for convenience:

For (x = 0), (y = x/2 = 0/2 = 0), giving us the point (0, 0).

For (x = 4), (y = x/2 = 5/2 = 2), giving us the point (5, 2.5).

Plot the points and draw the line:

Plot the points (0, 0) and (5, 2.5) on the coordinate plane and draw a straight line passing through these points. This line represents the boundary of the inequality y≥x/2.

Shade the region above the line:

Since the inequality is x ≤ 2y, we shade the region above the line y≥x/2. This shaded area will represent all the points that does not satisfy the inequality.

5. 3x - 2y ≥ 12

For the inequality (3x - 2y ≥ 12), we'll first rearrange the equation:

y ≤ (-12-3x)2

y ≤ (3/2)x - 6

Plot the boundary line y ≤ (3/2)x - 6:

To graph this line, rearrange the equation toy ≤ (3/2)x - 6 in slope-intercept form (y = mx + c. Choose suitable x values and calculate corresponding y values to plot the points.

Let's choose (x = 0) and (x = 4) for convenience:

For (x = 0), (y = 3/2(0) - 6 = -6), giving us the point (0, -6).

For (x = 4), (y = 3/2(4) - 6 = 6 - 6 = 0), giving us the point (4, 0).

Plot the points and draw the line:

Plot the points (0, -6) and (4, 0) on the coordinate plane and draw a straight line passing through these points. This line represents the boundary of the inequality y ≤ (3/2)x - 6.

Shade the region below the line:

Since the inequality is (3x - 2y ≥ 12), we shade the region below the line y ≤ (3/2)x - 6. This shaded area will represent all the points that does not satisfy the inequality.