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

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.

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

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

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.

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

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

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.

The above graph matches with the graph 3.

- y = x - 4

y = - x + 4

Choose values for x.

Plot the points on a graph.

The above graph matches with the Graph 4.

So, Graph 4 is the correct choice.

y = 3x - 4

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

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

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

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

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

y = x + 1

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

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

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

y < x + 1 ⇒ 0 < 0 + 1 ⇒ 0 < 1

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

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

y = 2x - 3

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

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

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

y ≥2x - 3 ⇒ 0 ≥ 2(0) - 3 ⇒ 0 ≥ - 3

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

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

y2 = x3 - 1 ⇒ y = 23x - 2

When x = 0, y = 23 (0) - 2 = - 2

When x = 3, y = 23(3) - 2 = 0

Thus, the points (0, -2) and (3, 0) are the solutions of the equation y2 = x3 - 1.

Draw a line passing through these points.

Therefore, graph 1, represents the equation y2 = x3 - 1.

y = - 34x + 3

When x = 0, y = - 34 (0) + 3 = 3

When x = 4, y = - 34(4) + 3 = 0

Thus, the points (0, 3) and (4, 0) are the solutions of the equation y = - 34 x + 3.

Draw a line passing through these points.

Therefore, graph 1 represents the equation y = - 34x + 3.

y = 43x - 1

When x = 3, y = 43(3) - 1 = 3

When x = 0, y = 43(0) - 1 = - 1

Thus, the points (0, - 1) and (3, 3) are the solution of the equation y = 43x - 1.

Draw a line passing through these points.

Therefore, graph 4, represents the equation y = 43x - 1.

y = - 45 = - 0.8

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

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.

Therefore, graph 2 represents the equation y = - 45

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

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

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

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

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

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

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

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