1.
Graph x + 3y ≤ 6, indicating the
solution set with crosshatching or shading. Explain how you determined where to
draw the line and shade the area that represents the solution set.

First of all, the boundary line of the solution set is the line x + 3y = 6 so find where it crosses the axes (i) it crosses the x-axis where y = 0 i.e. at x = 6 (ii) it crosses the y-axis where x = 0 i.e. 3y = 6 or y = 2 . Plot those two points and draw a line through them (and byond them in both directions). since the inequation is </=, the line is included so draw a solid line (you would draw a broken line if the 6 was not included). Since you want x + 3y </= 6, you want all the page under the line so shade everything below the line.