Question

Graph the inequality on the axes below.
5, x, plus, 2, y, is less than, minus, 16
5x+2y<−16 on a graph with two points

Answer 1

Step 1 — find the boundary line:
5x + 2y = −16.
x-intercept (y = 0): 5x = −16 → x = −16/5 = −3.2 → point (−3.2, 0).
y-intercept (x = 0): 2y = −16 → y = −8 → point (0, −8).

Step 2 — draw the line:
Plot (−3.2, 0) and (0, −8) and draw the straight line through them. Because the inequality is strict (<), draw the line dashed.

Step 3 — choose a test point to determine which side to shade:
Test (0,0): 5(0)+2(0)=0 which is not < −16, so do NOT shade the side containing (0,0).
Alternatively test (−4,0): 5(−4)+2(0)=−20 which is < −16, so shade the side that contains (−4,0).

Conclusion:
Graph the dashed line through (−3.2, 0) and (0, −8), and shade the half-plane on the side that contains (−4,0) (the region below/left of the line).