Question

monthly payment scheme in company y
the above graph shows the payment scheme that company y offers to each of its salesmen. according to this payment scheme, part of a salesman’s monthly payment p in thousand dollars is based on the sales s in thousand dollars they make during the specific month.
which of the following represents the relationship between p and s when 0 ≤ s ≤ 45?
○ p = 5s + 1.4
○ p = 0.1s + 1.4
○ p = 0.08s + 1.4
○ s = 1.4p + 5

Explanation:

Step1: Identify two points on the line

From the graph, when \( S = 0 \), \( P = 1.4 \); when \( S = 5 \), let's check the graph (assuming the second point is \( S = 5 \), \( P = 1.4 + 0.1\times5 = 1.9 \)? Wait, no, let's take two clear points. Let's take \( (S, P)=(0, 1.4) \) and \( (S, P)=(5, 1.9) \)? Wait, maybe better to use the slope formula. The slope \( m=\frac{\Delta P}{\Delta S} \). Let's take \( S = 0 \), \( P = 1.4 \) and \( S = 45 \), \( P = 6 \)? Wait, no, the graph: when \( S = 0 \), \( P = 1.4 \); when \( S = 5 \), \( P = 1.4 + 0.1\times5 = 1.9 \)? Wait, let's calculate the slope between \( (0, 1.4) \) and \( (5, 1.9) \): \( m=\frac{1.9 - 1.4}{5 - 0}=\frac{0.5}{5}=0.1 \). Wait, no, maybe another point. Wait, the options: let's test the options with \( S = 0 \). For option B: \( P = 0.08S + 1.4 \), when \( S = 0 \), \( P = 1.4 \), good. For option C: \( P = 0.1S + 1.4 \), when \( S = 0 \), \( P = 1.4 \), good. For option A: \( S = 1.4P + 5 \), when \( S = 0 \), \( 0 = 1.4P + 5 \), \( P = -5/1.4 \), not good. For option D: \( P = 5S + 1.4 \), when \( S = 0 \), \( P = 1.4 \), but when \( S = 1 \), \( P = 6.4 \), which is too big. Now test \( S = 5 \) in option B: \( P = 0.08\times5 + 1.4 = 0.4 + 1.4 = 1.8 \). In option C: \( P = 0.1\times5 + 1.4 = 0.5 + 1.4 = 1.9 \). Wait, maybe the graph has a point at \( S = 10 \), \( P = 2.4 \)? Let's check the slope. If \( S = 0 \), \( P = 1.4 \); \( S = 10 \), \( P = 2.4 \). Then slope \( m=\frac{2.4 - 1.4}{10 - 0}=\frac{1}{10}=0.1 \). So the equation is \( P - 1.4 = 0.1(S - 0) \), so \( P = 0.1S + 1.4 \). Let's check another point: \( S = 45 \), \( P = 0.1\times45 + 1.4 = 4.5 + 1.4 = 5.9 \approx 6 \), which matches the graph (since at \( S = 45 \), \( P \) is 6). So the correct equation is \( P = 0.1S + 1.4 \).

Step2: Verify with the options

• Option A: \( S = 1.4P + 5 \) → when \( S = 0 \), \( P = -5/1.4 \), invalid.
• Option B: \( P = 0.08S + 1.4 \) → slope 0.08, doesn't match our calculated slope 0.1.
• Option C: \( P = 0.1S + 1.4 \) → slope 0.1, y-intercept 1.4, matches.
• Option D: \( P = 5S + 1.4 \) → slope 5, way too steep, invalid.

Answer:

C. \( P = 0.1S + 1.4 \)