1. The inequality representing the scenario is \(1.25x + 2.50y < 10\).
2. Rearrange to solve for \(y\): \(2.50y < 10 - 1.25x\) or \(y < 4 - 0.5x\).
3. The graph of \(y < 4 - 0.5x\) is a line with a slope of \(- 0.5\) and a y-intercept of 4, with shading below the line (indicating less than).
4. The first graph matches this description, showing the line with a negative slope and shading below it.

Supplemental Knowledge

Linear inequalities are expressions that show the relationship between two expressions using inequality symbols (e.g., <, >, ≤, ≥). When graphing linear inequalities:

1. Identify the Inequality:
   • For Felix's spending scenario, the inequality is \(1.25x + 2.50y < 10\).
2. Graphing Steps:
   • Convert the inequality to an equation to find the boundary line: \(1.25x + 2.50y = 10\).
   • Determine intercepts by setting \(x\) and \(y\) to zero alternately.
   • Plot the boundary line on a graph.
   • Use a dashed line for "<" or ">" and a solid line for "≤" or "≥".
   • Shade the region that satisfies the inequality.
3. Intercepts Calculation:
   • For \(x\)-intercept (\(y = 0\)): \(1.25x = 10 \Rightarrow x = 8\)
   • For \(y\)-intercept (\(x = 0\)): \(2.50y = 10 \Rightarrow y = 4\)

Applied Knowledge

Similar to Felix's experience at a grocery store, you need to figure out your grocery expenses within your limited budget and decide how many items will fit within it. Visualizing linear inequalities helps visualize these constraints so as to make informed decisions.
Understanding this concept can assist in effectively managing finances by visualizing spending limits and making wise choices within those limits.

Mastering linear inequalities empowers you to make smart financial decisions by visualizing constraints and possibilities clearly. At UpStudy, we offer tools and resources to help you excel in algebra and beyond.
For precise calculations involving inequalities, try UpStudy’s Algebra Inequalities Calculator today!