To graph the inequality 6x + 3y ≤ 12, you will first need to convert the inequality into an equation to find its boundary line. This means you will set 6x + 3y = 12.
1. **Find the intercepts**:
– To find the x-intercept, set y = 0:
6x + 3(0) = 12 → 6x = 12 → x = 2.
– To find the y-intercept, set x = 0:
6(0) + 3y = 12 → 3y = 12 → y = 4.
2. **Plot the intercepts**: You will plot the points (2, 0) and (0, 4) on the graph.
3. **Draw the boundary line**: Since the inequality is ‘less than or equal to’ (≤), you will draw a solid line connecting these two points to indicate that points on this line are included in the solution.
4. **Shade the appropriate area**: Since the inequality is ‘less than or equal to’, you will shade the area below the line. This shaded area represents all the points (x, y) that satisfy the inequality 6x + 3y ≤ 12.
By following these steps, you’ll accurately graph the inequality and visually represent the solution set.