Final answer:
To solve the inequalities by graphing, transform each inequality into an equation form, plot the lines on the graph, and identify the overlapping region that satisfies both inequalities. The lines are 5x + 2y ≥ 3 and y ≥ x, with appropriate slopes and y-intercepts.
Step-by-step explanation:
To solve the inequalities by graphing, we need to transform each inequality into a graphable equation form and then use the properties of the lines to find the solution set. The inequalities in question are:
Let's graph each inequality one by one:
- For the inequality 5x + 2y ≥ 3, convert it to y-intercept form (y = mx + b) by isolating y: 2y ≥ -5x + 3, y ≥ -2.5x + 1.5. This line has a slope (m) of -2.5 and a y-intercept (b) of 1.5.
- To graph y ≥ x, simply draw a line with a slope of 1 and a y-intercept of 0, which is the identity line where y equals x.
The solution to the system of inequalities will be the region on the graph where both conditions are satisfied, typically above the lines in this case because both inequalities are greater than or equal to.
Always label your graph with f(x) and x, and select an appropriate scale for the x and y axes to ensure all important points and lines are visible on the graph.
The provided figures and instructions on slope and graphing help us understand how to plot each line based on their equations. Using the slope-intercept form, we graph the lines and identify the intersection or overlapping regions that satisfy both inequalities.