Final answer:
To graph the inequality 4x + 5y ≤ 20, find the boundary line by plotting the y-intercept (0,4) and x-intercept (5,0), draw a solid line to connect these points, and shade the area beneath. Label the axes with x and f(x), and scale up to the maximum values of x and y as 20.
Step-by-step explanation:
To graph the solution to the inequality 4x + 5y ≤ 20, we need to find the boundary line, which is determined by the equation 4x + 5y = 20. Here's how to proceed:
First, solve for y in terms of x to get the slope-intercept form: y = –20/5 - 4/5x. This simplifies to y = -4x + 4.
The y-intercept is when x=0, so it is at the point (0,4). The x-intercept is when y=0, so it is at the point (5,0).
Plot these intercepts on the graph, labeling the x and y axes. The x-axis is labeled with variable x and the y-axis can be labeled with function f(x) for simplicity, even though it is not a function graph.
Draw a solid line to connect these points because the inequality includes the boundary (due to the ≤ sign).
Since the inequality is ≤, shade the area below the line which represents all solutions (x, y) that satisfy the inequality.
The graph should be accurately scaled along the x and y axes, remembering that the maximum value of x and y needed is 20 for depicting this inequality.
Since the function f(x) refers to a constant value in this context, we can understand it as the y-value of 20 when x = 0.
The relationship between x and y in this inequality showcases the dependence of y on x.
While we don't often label graphs of inequalities with an f(x), for the purpose of this example we could consider the boundary line as the graph of f(x) when f(x) = -4x + 4, restricted for 0 ≤ x ≤ 20.