Use the image to answer the question.

A graph with the x-axis representing scoops of red paint ranging from 0 to 12 in increments of 1 and the y-axis representing scoops of yellow paint ranging from 0 to 30 in increments of 1 shows seven plotted points, 5 for option A and 2 option B. Option A has the following points: left parenthesis 2 comma 5 right parenthesis; left parenthesis 4 comma 10 right parenthesis; left parenthesis 6 comma 15 right parenthesis; left parenthesis 8 comma 20 right parenthesis; and left parenthesis 10 comma 25 right parenthesis. Option B has the following points: left parenthesis 5 comma 11 right parenthesis and left parenthesis 10 comma 22 right parenthesis.

Which coordinate pair should be plotted next for Option B to keep the ratio the same?

(1 point)
Responses

(11, 23)
left parenthesis 11 comma 23 right parenthesis

(11, 33)
left parenthesis 11 comma 33 right parenthesis

(15, 23)
left parenthesis 15 comma 23 right parenthesis

(15, 33)

1 answer

To determine the correct coordinate pair to keep the ratio the same for Option B, we need to analyze the points already established.

The two points for Option B are:

  1. \( (5, 11) \)
  2. \( (10, 22) \)

Let's find the ratio of yellow paint to red paint in both points:

  • For the point \( (5, 11) \): \[ \text{Ratio} = \frac{11}{5} \]

  • For the point \( (10, 22) \): \[ \text{Ratio} = \frac{22}{10} = \frac{11}{5} \]

Both points have a consistent ratio of \( \frac{11}{5} \).

Now, to keep the same ratio, we can use the formula: \[ y = \frac{11}{5} \times x \]

Now we need to check the response options:

  1. \( (11, 23) \): \[ y = \frac{11}{5} \times 11 = \frac{121}{5} = 24.2 \] (Not \(23\))

  2. \( (11, 33) \): \[ y = \frac{11}{5} \times 11 = \frac{121}{5} = 24.2 \] (Not \(33\))

  3. \( (15, 23) \): \[ y = \frac{11}{5} \times 15 = \frac{165}{5} = 33 \] (This works for \(33\))

  4. \( (15, 33) \): \[ y = \frac{11}{5} \times 15 = \frac{165}{5} = 33 \] (This works for \(33\) as well)

Among the available options preserving the ratio of \( \frac{11}{5} \):

The correct answer is \( \text{(15, 33)} \).