Question

Which linear inequality is represented by the graph?

y < Two-thirdsx + 3
y > Three-halvesx + 3
y > Two-thirdsx + 3
y < Three-halvesx + 3

Answer 1

I don’t see the graph — could you upload it or describe it (the boundary line and which side is shaded)?

If you want to decide it yourself, here are quick steps:

1. Identify the boundary line in slope-intercept form y = mx + b:
- If the line passes through (0, 3) and rises 2 for every 3 right, m = 2/3 so boundary is y = (2/3)x + 3.
- If it rises 3 for every 2 right, m = 3/2 so boundary is y = (3/2)x + 3.

2. Check whether the shading is above or below the line:
- Shading above the line → use “>”
- Shading below the line → use “<”

3. Check whether the boundary line is dashed (strict inequality < or >) or solid (≤ or ≥). All four choices you gave are strict, so a dashed line would match them.

So, for example:
- If boundary is y = (2/3)x + 3 and the region below is shaded → y < (2/3)x + 3.
- If boundary is y = (3/2)x + 3 and region above is shaded → y > (3/2)x + 3.

Send the graph or a short description and I’ll pick the correct choice.