Graph the inequality.
3x + y ≤ 5
To graph a linear inequality in two variables x and y when the coefficient of y is not a zero.
1. Write the given inequality as an equivalent inequality that has y alone on one side.
3x + y ≤ 5
y ≤ -3x + 5
2. Graph the related linear equation. Use a dashed line if the inequality involves < or >. Use solid line if the inequality involves ≤ or ≥.
graph y = -3x + 5. Since the inequality symbol used is ≤, use
solid line.
3. Test a point in each half-plane to see which satisfies the inequality.
y ≤ -3x + 5, Test (0,0) when x = 0 and y = 0
0 ≤ 0 + 5
0 ≤ 5 ---------> true
4. Shade the appropriate half-plane.
Since (0,0) satisfies the inequality that means you shade where the
(0,0) is located (the left side of the line formed)
The graph looks like this:
Remember to use solid line and shade the left side of the line.
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