Question

The table shows come of the solutions for an inequality related to the line shown in the graph. Which inequality describes the solution set?

Answer 1

Option A:
`y\geq x-3`

Explanation:

The graph line shown in the graph cuts to the x-axis at
`x = 3` and cuts the y-axis at
`y = -3`. Therefore the equation for this line is:

`y = x-3`

All the points shown in the table are located above the line
`y = x-3`, except for the point (2, -1). This point belongs to the equation of the line, that is, it is on the line. Therefore, the region represented by the points in the table must include the points that are on the line. Therefore we can discard options C and D.

The points shown in the table are above the graph of the line, therefore, we can say that the region is composed of all the values of y that are greater than those of the line
`y = x-3`.

Then the inequality is:

`y\geq x-3`