Question

Which inequality does this graph show?

A. 3y + x < –x – y – 8
B. 3y – x < 3x – y – 8
C. 3y + x < 3x + y – 8
D. 3y + x < 3x – y – 8

Answer 1

The inequality 3y + x < 3x - y - 8 is represented by option D.

Explanation:

The inequality 3y + x < 3x - y - 8 is represented by option D.

To see this, we can rearrange the inequality to get all the x and y terms on one side, like so:

3y + x < 3x - y - 8

4y < 2x - 8

2y < x - 4

y < (1/2)x - 2

This shows that y is less than a linear function of x, with a slope of 1/2 and a y-intercept of -2. Visually, this represents a downward-sloping line on a graph. Therefore, option D is the correct answer.