Final answer:
To derive the graph of the inequality 4x + 6y ≤ 24, rewrite the inequality in slope-intercept form and graph the line with a slope of -2/3 and a y-intercept of 4, shading the region below the line.
Step-by-step explanation:
To derive the graph of the inequality 4x + 6y ≤ 24, we can start by rewriting the inequality in slope-intercept form where y is isolated on one side of the equation:
6y ≤ -4x + 24
y ≤ -(2/3)x + 4
This tells us that the slope of the line is -2/3 and the y-intercept is 4. To graph this inequality, we can plot the y-intercept at (0,4) and then use the slope to find additional points. Since the inequality includes '≤', we will shade the region below the line to represent all the points that satisfy the inequality.