Which graph represents viable values for y = 2X, Where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of lhe rice? Save and Exit suul Nuubi; ulelun Nenr
The Correct Answer and Explanation is:
To determine which graph represents viable values for the equation y = 2x, where:
- x is the number of pounds of rice scooped and purchased from a bulk bin, and
- y is the total cost of the rice in dollars,
we can break down what this relationship means and describe what the correct graph should look like.
🔍 Understanding the Equation:
The equation y = 2x tells us that:
- For every 1 pound of rice, the cost is $2.
- This is a linear relationship where the cost increases proportionally with the number of pounds.
- The slope of the line is 2, meaning the price increases by $2 for each additional pound.
- The y-intercept is 0, because if you scoop 0 pounds, the total cost is $0.
✅ Key Characteristics of the Correct Graph:
- It is a straight line that starts at the origin (0, 0).
- The line rises steadily, with a slope of 2 (for every 1 unit increase in x, y increases by 2).
- The graph only makes sense in Quadrant I (where both x and y are positive), since you cannot scoop a negative amount of rice or pay a negative amount of money.
- The x-axis represents pounds of rice (must be ≥ 0), and the y-axis represents total cost (must be ≥ 0).
- The domain and range are both non-negative real numbers.
❌ What to Avoid in the Graph:
- Any line that doesn’t start at (0, 0).
- A graph that curves instead of forming a straight line.
- A line that goes downward (which would indicate a negative slope or decreasing price with more rice).
- Points in the negative x or y direction, which are not viable in this real-world context.
✅ Conclusion:
The correct graph will be a straight line starting at (0, 0) with a slope of 2, located in the first quadrant only, showing a constant price of $2 per pound of rice.
