Final answer:
In the inequality 5x - y ≤ 1, shading on the left side of the boundary represents the solution set because it includes the origin (0,0), which satisfies the inequality. The boundary line has a negative slope, and the correct side for shading is determined by testing a point not on the line.
Step-by-step explanation:
The inequality 5x − y ≤ 1 represents a region in the coordinate plane that includes all points that satisfy the inequality. To graph the inequality, first draw the boundary line for the equation 5x − y = 1. This boundary line is a straight line with a negative slope because the coefficient of x is positive and the coefficient of y is negative. To determine which side of the line to shade, pick a test point that is not on the line. A common choice is the origin (0,0) unless the line passes through the origin. Plugging in (0,0) into the inequality 5(0) - 0 ≤ 1 gives 0 ≤ 1, which is true, so we shade the side that includes the origin.
Since shading on the left side of the boundary includes the origin and all points that satisfy the inequality, the correct answer is option (a): Shading on the left side represents the solution set for the inequality.