Step 1: Create Equations

Let us consider a scenario where two quantities are related. For instance:

1. Scenario 1 (Linear Relationship): A company sells two products, $x$ and $y$. The total revenue is determined by the selling price of $x$ and $y$. If the price of product $x$ is $5 and the price of product $y$ is $3, the total revenue equation can be written as: $5x + 3y = R$ where $R$ is the total revenue.

2. Scenario 2 (Non-linear Relationship): Suppose the cost of producing $x$ and $y$ units of two products is given by: $C = x^2 + y^2$ where $C$ represents the total cost.

Step 2: Graph the Equations

To graph these equations:

Example 1: $5x + 3y = R$

• Assign a fixed value for $R$, say $R = 15$.
• Rewrite the equation: $5x + 3y = 15$, or $y = \frac{15 - 5x}{3}$.
• Plot points by assigning values to $x$, such as $x = 0, 1, 2$, and solving for $y$.

Example 2: $x^2 + y^2 = C$

• Assign a fixed value for $C$, say $C = 25$.
• Rewrite the equation: $x^2 + y^2 = 25$, representing a circle with radius 5.

Step 3: Graphing Process

Below is the guidance to plot these equations:

1. Label Axes: Label the $x$- and $y$-axes appropriately, setting scales.
2. Choose Points: Calculate points for each equation to represent the relationships graphically.
3. Draw the Graphs:
   • A straight line for the linear equation ($5x + 3y = 15$).
   • A circle for the quadratic equation ($x^2 + y^2 = 25$).

Visualization

If you upload a photo or request detailed plots, I can help create and display these graphs for better understanding.

---

Would you like help graphing these or solving another example?

---

Related Questions:

1. Can you write an equation to represent a parabola?
2. How would you interpret the graph of $x^2 + y^2 = 25$?
3. How do you find intercepts for a linear equation like $5x + 3y = 15$?
4. How can the equation of a circle be extended to include shifts in the center?
5. What does the slope of a line signify in a graph?

---

Tip:

To ensure accurate graphing, always choose a reasonable scale for the axes to clearly display the relationship between variables.