Question

How do you graph the inequality `3/4x + 1/4y > 1`?

Answer 1

Draw the straight line `(3x+y)/4=1` that passes through`(4/3, 0) and (0, 4)`. Shade the region above this line in the positive y-direction. Enter therein the given inequality.

Explanation:

The given inequality can be rearranged to the form `y>4-3x`

Draw the straight line `y=4-3x` that passes through`(4/3, 0) and (0, 4)`.

Shade the region above this line in the positive y-direction.

Enter therein the given inequality.

For any point (x, y) in the shaded region, `y>4-3x`, and so, `y/4+(3x)/4>1`.