Question

Graph the inequality on the axes below.
minus, 5, x, plus, 3, y, is less than or equal to, minus, 12
−5x+3y≤−12

Answer 1

Step 1 — Put the inequality 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, so (2.4, 0).
- Another easy point: x = 3 → y = 1, so (3, 1).

Because the inequality is ≤, draw the boundary as a solid line.

Step 3 — Determine which side to shade:
Test (0,0): −5(0)+3(0) ≤ −12 gives 0 ≤ −12 (false). So (0,0) is not in the solution set. That means you should shade the side of the line opposite the origin — i.e., the region below the line y = (5/3)x − 4 (all points with y less than or equal to the line).

Summary for the graph:
- Solid line through (0, −4) and (2.4, 0) with slope 5/3.
- Shade the region below that line (not the region containing the origin).

If you want, I can produce a plotted image of this.