Question

−5x+3y≤−12 graph the inequality

Answer 1

Step 1 — put in slope‑intercept form:
-5x + 3y ≤ −12
3y ≤ 5x − 12
y ≤ (5/3)x − 4

Step 2 — draw the boundary line y = (5/3)x − 4
- y‑intercept: (0, −4)
- x‑intercept: set y = 0 → (5/3)x − 4 = 0 → x = 12/5 = 2.4 → (2.4, 0)
- slope = 5/3, so from (0, −4) go right 3 and up 5 to get another point (3, 1).
- Because the inequality is ≤, draw the boundary as a solid line.

Step 3 — decide which side to shade
- Test the origin (0,0): -5(0)+3(0) ≤ −12 → 0 ≤ −12, false. So do NOT shade the side containing the origin.
- Shade the side below/left of the line (the side that gives smaller y-values), i.e. the half‑plane of points satisfying y ≤ (5/3)x − 4.

If you want, I can draw and send a plotted image of this graph.