Question

Graph the inequality y is greater than or equal to one third times x plus one.

The graph shows a solid line that passes through negative 3 comma 0 and 0 comma 1, with shading above the line.
The graph shows a solid line that passes through negative 3 comma 0 and 0 comma 1, with shading below the line.
The graph shows a dashed line that passes through negative 3 comma 0 and 0 comma 1, with shading above the line.
The graph shows a dashed line that passes through negative 3 comma 0 and 0 comma 1, with shading below the line.

Answer 1

The graph shows a solid line that passes through (-3, 0) and (0, 1), with shading below the line

Answer 2

Explanation:

The inequality y ≥ (1/3)x + 1 represents all the points that lie on or above the line y = (1/3)x + 1.

To graph this line, we can first plot the y-intercept at (0, 1). From there, we can use the slope of (1/3) to find additional points on the line.

For example, if we move one unit to the right (x = 1), we would move up one-third units (y = 1 + 1/3), giving us the point (1, 4/3). Similarly, if we move two units to the right (x = 2), we would move up two-thirds units (y = 1 + 2/3), giving us the point (2, 5/3).

To indicate that the inequality includes points on the line, we use a solid line.

Finally, to determine which region to shade, we can test a point not on the line. For example, the point (0, 0) is below the line, so we shade the region above the line.

Therefore, the correct answer is: The graph shows a solid line that passes through negative 3 comma 0 and 0 comma 1, with shading above the line.