Question

Which graph represents the solution of
2
x
−
5
y
<
3
?


image.png


image.png


image.png


image.png

Answer 1

Rewrite the inequality:

2x − 5y < 3
⇒ −5y < 3 − 2x
⇒ multiply by −1 (flip inequality): 5y > −3 + 2x
⇒ y > (2/5)x − 3/5.

So the boundary is the line y = (2/5)x − 3/5, drawn as a dashed line (because the inequality is strict), and the solution is the region above that line. A quick check: (0,0) satisfies 0 < 3, so the region containing the origin is the correct shading.

Pick the image that shows the dashed line y = (2/5)x − 3/5 with the region above it shaded (the one that shades the origin).