Graph The Inequalities And Show The Shaded Solution Region

Graph the inequalities and show (shade in) The solution region. 7 y ≤ 21 G

The actual assignment question requires plotting the inequality 7y ≤ 21 and showing the solution region by shading. Although the text appears partially garbled with repetitions and unrelated characters, the core task in this context is to graph the inequality 7y ≤ 21 and illustrate the solution area visually. This involves rearranging the inequality into a more familiar form, plotting the boundary line, and shading the appropriate region that satisfies the inequality.

Paper For Above instruction

The task of graphing inequalities such as 7y ≤ 21 involves understanding the relationship between the algebraic form and its graphical representation. The primary goal is to accurately plot the boundary line (or curve) that corresponds to the equality case and then shade the the region that satisfies the inequality.

First, to clarify the inequality: 7y ≤ 21, we divide both sides by 7 (which is positive, so the inequality direction remains unchanged), resulting in y ≤ 3. This simplified form makes it easier to understand and graph: it indicates that the solution set includes all points where the y-coordinate is less than or equal to 3.

Next, we plot the boundary line y = 3. Because the inequality is ≤ (less than or equal to), the boundary line y=3 should be drawn as a solid line, indicating that points on this line are also part of the solution set. To graph the line, I mark the point (0,3) and draw a straight line horizontally across the graph at y=3.

Once the boundary is established, shading the solution region involves shading all the points where y ≤ 3. Since y is less than or equal to 3, the shading should be below or on the line y=3. The area below (or south of) y=3 runs infinitely downward, including the line itself.

Practically, for accurate graphing, select multiple points with y-values less than 3, such as (0,2), (1,0), and (-2,-5), and confirm that they satisfy y ≤ 3. Plot these points to help visualize the area. Shade uniformly the entire region below y=3, extending to the axes or edges of the graph, emphasizing that all those points are solutions.

The significance of this graph is that it visually communicates the entire set of solutions to the inequality 7y ≤ 21, which encompasses all points where y is at most 3. This is essential in understanding more complex inequalities involving multiple variables or different boundary shapes. Proper shading and boundary representation are critical for clarity and correctness in depicting solutions graphically.

References

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