Question

Which inequality is represented by the graph?

Answer 1

B: 4/5x -2y ≥ 3

Explanation:

The first thing I always look for is the y-intercept which in this case is around -1.5 (-
`1(1)/(2)`). That will be your constant (b) in y = mx + b. Then calculate the slope which will be your m in the equation. Visually, I would estimate it is around
`(2)/(5)`. So now, your equation is y =
`(2)/(5)`x -1
`(1)/(2\\)`. Next we want to figure out what the inequality will be. The shaded part is underneath the line, which means that y must be less than where the line is. Therefore the inequality will be y ≤
`(2)/(5)`x -1
`(1)/(2\\)`.

Now in this question, the answers available are not in this form. The next step would be to multiply every part of the inequality by 2 (it is essential that all parts are multiplied) so that you get 2y ≤
`(4)/(5)`x -3. The last step is to rearrange the inequality so that it matches the answers on the question.

3 ≤
`(4)/(5)`x - 2y

`(4)/(5)`x - 2y ≥ 3