Enter an equation in the form y = kx that represents the relationship between x and y.

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Understand the Problem

The question is asking to determine the equation of a proportional relationship between the number of calories (y) and the number of grapes (x) based on the information given in the graph.

Answer

The equation is \( y = \frac{3}{2}x \).
Answer for screen readers

The equation representing the relationship is ( y = \frac{3}{2}x ).

Steps to Solve

  1. Identify the point on the graph The graph shows the point $(150, 225)$, meaning that for 150 grapes, there are 225 calories. This point will be used to find the proportionality constant.

  2. Determine the proportionality constant The proportional relationship can be expressed as $y = kx$, where $k$ is the proportionality constant. Using the point identified: $$ k = \frac{y}{x} = \frac{225}{150} $$

  3. Calculate the value of k Now, simplify the fraction to find the value of $k$: $$ k = \frac{225 \div 75}{150 \div 75} = \frac{3}{2} $$

  4. Write the equation Substituting the value of $k$ back into the relationship gives us: $$ y = \frac{3}{2}x $$

The equation representing the relationship is ( y = \frac{3}{2}x ).

More Information

This equation shows that for every grape consumed, the calories increase by 1.5 times, indicating a direct proportional relationship between the number of grapes and calories.

Tips

  • Forgetting to simplify the fraction when calculating ( k ).
  • Not recognizing that the point given on the graph corresponds to the values of ( x ) and ( y ) needed for the calculations.
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