Final answer:
The linear inequality representing a budget of $44 for albums and movies, with albums at $5 and movies at $12, is 5x + 12y <= 44. The graph would show a line passing through points (8, 0) and (0, 3) with the area below and to the left shaded to represent all affordable combinations.
Step-by-step explanation:
To represent the situation where a student has $44 to spend on music and movie downloads with albums costing $5 each and movies costing $12 each, we can write a linear inequality. Let x represent the number of albums and y represent the number of movies. The inequality that represents the spending limit is:
5x + 12y ≤ 44
To graph this inequality, we first identify the intercepts. The album intercept (x-intercept) occurs when no money is spent on movies (y=0), so we spend all $44 on albums. Dividing the total budget by the cost of an album gives us:
44 / 5 = 8.8
Since we can't download a fraction of an album, the maximum number of full albums is 8. Similarly, the movie intercept (y-intercept) occurs when no money is spent on albums (x=0). Calculating this gives us:
44 / 12 ≈ 3.67
The maximum number of full movies we can download, therefore, is 3. The inequality graph will be a line that pass through the points (8, 0) and (0, 3), but since we're dealing with an inequality, we'll shade the area below and to the left of the line to indicate all possible combinations of albums and movies that the student can afford.