Step: 1

The boundary line of the half-plane is dashed if the inequality is < or > and solid if the inequality is ≤ or ≥.

Step: 2

For the inequalities 4x - y ≥ 6, 4x + 5y ≤ 6 and x + 4y ≤ 6 the boundary line of the half-plane is solid as they contain ≥ and ≤ symbols.

Step: 3

For the inequality 4x + y > 6 the boundary line of the half-plane is dashed as it contains > symbol.

Correct Answer is : 4x + y > 6

Step: 1

The boundary line of the half-plane is dashed if the inequality is < or > and solid if the inequality is ≤ or ≥.

Step: 2

For the inequalities 6x - 4y > 9, 2x + 5y < 4, and 6x + 5y < 9 the boundary line of the half-plane is dashed as they contain > and < symbols.

Step: 3

For the inequality 2x + 5y ≤ 4 the boundary line of the half-plane is solid as it contains ≤ symbol.

Correct Answer is : 2x + 5y ≤ 4

Step: 1

The x -coordinate is always - 2, regardless of the value of y .

Step: 2

The graph of the equation x = - 2 is a vertical line 2 units to the left of the y -axis as shown in the following graph.

Step: 3

The above graph matches with the graph 3.

Correct Answer is : Graph 3

Step: 1

- y = x - 4

[Original equation.]

Step: 2

[Apply the slope-intercept form, y = m x + c .]

Step: 3

Choose values for x .

Step: 4

Plot the points on a graph.

Step: 5

The above graph matches with the Graph 4.

Step: 6

So, Graph 4 is the correct choice.

Correct Answer is : Graph 4

Step: 1

[Write the corresponding equation of the given inequality.]

Step: 2

The equation is in slope-intercept form y = mx + b , where m is the slope and b is the y-intercept.

Step: 3

Graph the corresponding equation using the slope and y-intercept. As the inequality involves '≥', use a solid line.

Step: 4

Test a point, which is not on the boundary line. Test (0, 0) in the inequality.

y ≥ 3x - 4 ⇒ 0 ≥ 3(0) - 4 ⇒ 0 ≥ - 4

[True.]

Step: 5

Since the inequality is true for (0, 0), shade the region that contains (0, 0).

Step: 6

Therefore, graph 4 represents the inequality y ≥3x - 4.

Correct Answer is : Graph 4

Step: 1

[Write the corresponding equation of the given inequality.]

Step: 2

The equation is in slope-intercept form y = mx + b , where m is the slope and b is the y -intercept.

Step: 3

Graph the corresponding equation using the slope and y-intercept. As the inequality involves '<', use a dashed line.

Step: 4

Test a point, which is not on the boundary line. Test (0, 0) in the inequality.

Step: 5

[True.]

Step: 6

Since the inequality is true for (0, 0), shade the region that contains (0, 0).

Step: 7

Therefore, graph 2 represents the inequality y < x + 1.

Correct Answer is : Graph 2

Step: 1

[Write the corresponding equation of the given inequality.]

Step: 2

The equation is in slope-intercept form y = mx + b , where m is the slope and b is the y - intercept.

Step: 3

Graph the corresponding equation using the slope and y - intercept. As the inequality involves '≥', use a solid line.

Step: 4

Test a point, which is not on the boundary line. Test (0, 0) in the inequality.

Step: 5

[True.]

Step: 6

Since the inequality is true for (0, 0), shade the region that contains (0, 0).

Step: 7

Therefore, graph 3 represents the inequality y ≥ 2x - 3

Correct Answer is : Graph 3

Step: 1

[Multiply by 2 on both sides of the equation.]

Step: 2

When x = 0, y = 2 3 (0) - 2 = - 2

[Substitute x = 0 in the equation.]

Step: 3

When x = 3, y = 2 3 (3) - 2 = 0

[Substitute x = 3 in the equation.]

Step: 4

Thus, the points (0, -2) and (3, 0) are the solutions of the equation y 2 = x 3 - 1.

Step: 5

Draw a line passing through these points.

Step: 6

Therefore, graph 1, represents the equation y 2 = x 3 - 1.

Correct Answer is : Graph 1

Step: 1

Step: 2

When x = 0, y = - 3 4 (0) + 3 = 3

[Substitute x = 0 in the equation.]

Step: 3

When x = 4, y = - 3 4 (4) + 3 = 0

[Substitute x = 4 in the equation..]

Step: 4

Thus, the points (0, 3) and (4, 0) are the solutions of the equation y = - 3 4 x + 3.

Step: 5

Draw a line passing through these points.

Step: 6

Therefore, graph 1 represents the equation y = - 3 4 x + 3.

Correct Answer is : Graph 1

Step: 1

Step: 2

When x = 3, y = 4 3 (3) - 1 = 3

[Substitute x = 3 in the equation.]

Step: 3

When x = 0, y = 4 3 (0) - 1 = - 1

[Substitute x = 0 in the equation.]

Step: 4

Thus, the points (0, - 1) and (3, 3) are the solution of the equation y = 4 3 x - 1.

Step: 5

Draw a line passing through these points.

Step: 6

Therefore, graph 4, represents the equation y = 4 3 x - 1.

Correct Answer is : Graph 4

Step: 1

[Simplify the equation.]

Step: 2

The y - coordinate is always - 0.8, regardless of the value of x .

Step: 3

Thus, the graph of the equation y = - 0.8 is a horizontal line which is 0.8 units below the x -axis as shown in the graph.

Step: 4

Therefore, graph 2 represents the equation y = - 4 5

Correct Answer is : Graph 2

Step: 1

The x - intercept is 1. Therefore, the line crosses the x -axis at a point (1, 0).

Step: 2

The y -intercept is -2. Therefore, the line crosses the y -axis at a point (0, -2).

Step: 3

Plot the points (1, 0) and (0, -2) and draw a line through them.

Step: 4

Therefore, graph 4 represents the graph of the equation whose x -intercept is 1 and y -intercept is -2.

Correct Answer is : Graph 4

Step: 1

The x - intercept is -3. Therefore, the line crosses the x -axis at a point (-3, 0).

Step: 2

The y -intercept is 1. Therefore, the line crosses the y -axis at a point (0, 1).

Step: 3

Plot the points (-3, 0) and (0, 1) and draw a line through them.

Step: 4

Therefore, graph 1 represents the graph of the equation whose x -intercept is -3 and y -intercept is 1.

Correct Answer is : Graph 1

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