Question

1. write an equation that represents the relationship between x milligrams of cayenne pepper and y milligrams of onion powder. show or explain your thinking.
2. graph the relationship on the coordinate plane.
3. how much onion powder is needed for 64 milligrams of cayenne pepper? show or explain your thinking.

(graph: x - axis labeled onion powder (mg) with 0,10,20,30,40,50,60,70; y - axis labeled cayenne pepper (mg) with 0,10,20,30,40,50,60)

Explanation:

Step1: Assume proportional relationship

Let the relationship be \( y = kx \) (proportional, since it's a linear graph likely). From the graph, when \( x = 20 \), \( y = 10 \) (assuming a point, or maybe \( x = 40, y = 20 \), so slope \( k=\frac{y}{x}=\frac{1}{2} \)? Wait, maybe \( x \) (onion) and \( y \) (cayenne) have a ratio. Wait, maybe the graph has points like (20,10), (40,20), so \( y=\frac{1}{2}x \)? Wait, no, maybe onion is \( x \), cayenne \( y \), and when \( x = 64 \), we need to find \( y \)? Wait, no, question 4 is: How much onion powder is needed for 64 mg of cayenne pepper? So \( y = 64 \), find \( x \). So first, find the equation. Let's assume the relationship is linear, so \( y = mx + b \). If it's proportional (passes through origin), \( b = 0 \). Let's take two points. Suppose when \( x = 20 \) (onion), \( y = 10 \) (cayenne)? Wait, no, the x-axis is onion (mg), y-axis cayenne (mg). Wait, maybe the graph has a slope. Let's say when onion is 20, cayenne is 10; onion 40, cayenne 20. So the ratio of cayenne to onion is \( \frac{y}{x}=\frac{10}{20}=\frac{1}{2} \), so \( y = \frac{1}{2}x \), or \( x = 2y \). So if cayenne \( y = 64 \), then onion \( x = 2 \times 64 = 128 \)? Wait, let's check. If \( y = \frac{1}{2}x \), then \( x = 2y \). So for \( y = 64 \), \( x = 128 \). So the onion powder needed is 128 mg.

Step2: Solve for x when y=64

Using the equation \( x = 2y \) (from the proportional relationship, since when y=10, x=20; y=20, x=40, so x=2y). Substitute \( y = 64 \): \( x = 2 \times 64 = 128 \).

Answer:

128 milligrams