Question

a manufacturing machine has two processes. one of them is repeated 4 times and the second only once. the entire cycle can take no longer than 3 minutes. which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

Explanation:

Step1: Define variables

Let $x$ = time for 1 repeat process, $y$ = time for single process.

Step2: Set up inequality

Total time ≤ 3 minutes: $4x + y \leq 3$

Step3: Rewrite in slope-intercept form

Rearrange to $y \leq -4x + 3$

Step4: Analyze the graph

• Boundary line: $y = -4x + 3$, slope = -4, y-intercept = 3.
• Shading: Below the line (≤), and only positive $x,y$ (time can't be negative). The top graph matches this: it has a line with steep negative slope starting at (0,3), shading below/right, and aligns with non-negative time values.

Answer:

The top (first) graph with the line $y = -4x + 3$ and shaded region below/right of the line (covering non-negative $x,y$ values) is the correct representation.