Graph x-3y<=0

Problem

x−3*y≤0

Solution

1. Isolate the y-variable to rewrite the inequality in slope-intercept form.

x≤3*y

1/3*x≤y

y≥1/3*x

2. Identify the boundary line by replacing the inequality symbol with an equals sign.

y=1/3*x

3. Determine the line style based on the inequality symbol. Since the inequality is ≥ (greater than or equal to), the boundary line is solid.

4. Find the slope and y-intercept of the boundary line. The slope is m=1/3 and the y-intercept is (0,0)

5. Determine the shaded region by testing a point not on the line, such as (0,1)

1≥1/3*(0)

1≥0

Since the statement is true, shade the region containing the point (0,1) which is above the line.

Final Answer

y≥1/3*x

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