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Use the image to answer the question.

A coordinate plane shows an x-axis ranging from 0 to 10 in increments of 2 and a y-axis ranging from 0 to 15 in increments of 3. The plotted points form an upward diagonal line. The first data point is at left parenthesis 2 comma 3 right parenthesis. The fourth data point is at left parenthesis 8 comma 12 right parenthesis. Two points in between the given points are left blank with only the parenthesis. The X-axis value of the second data points are the scale value next to 2 and the Y-axis value next to 3. The X-axis value of the third data points are the scale value next to 4 and the Y-axis value next to 6.

Choose the coordinate pair to plot on the coordinate plane so the ratio stays equivalent.

(1 point)
Responses

(4, 6)
Left Parenthesis 4 comma 8 Right Parenthesis

(6, 4)
Left Parenthesis 8 comma 4 Right Parenthesis

(4, 10)
Left Parenthesis 4 comma 10 Right Parenthesis

(3, 8)

11 answers

To find a coordinate pair that maintains the ratio consistent with the given points on the line, we should first determine the relationship between the x-values and y-values.

From the points provided:

  • The first point is (2, 3).
  • The fourth point is (8, 12).

We can observe the following:

  • The x-values are 2, 4, 6, 8 — increasing by 2.
  • The y-values are 3, 6, 9, 12 — increasing by 3.

From this, we can see that for every increase of 2 in the x-value, there is an increase of 3 in the y-value. This gives us a consistent ratio of:

\[ \frac{y}{x} = \frac{3}{2} \quad \text{or} \quad y = \frac{3}{2}x. \]

Now, let’s check the provided response options to see which pair maintains this ratio:

  1. (4, 6): \[ \frac{6}{4} = \frac{3}{2} \quad \text{(Valid)} \]

  2. (4, 8): \[ \frac{8}{4} = 2 \quad \text{(Not valid)} \]

  3. (6, 4): \[ \frac{4}{6} = \frac{2}{3} \quad \text{(Not valid)} \]

  4. (8, 4): \[ \frac{4}{8} = \frac{1}{2} \quad \text{(Not valid)} \]

  5. (4, 10): \[ \frac{10}{4} = \frac{5}{2} \quad \text{(Not valid)} \]

  6. (3, 8): \[ \frac{8}{3} \quad \text{(Not valid)} \]

Based on this analysis, the only valid coordinate pair that maintains the ratio is:

(4, 6)

are u sure

Yes, let's double-check the calculations to ensure accuracy:

Given the earlier points:

  1. The first point: (2, 3)
  2. The fourth point: (8, 12)

We identified the relationship as:

  • For every increase of 2 in the x-value, there is an increase of 3 in the y-value.

This leads to the linear relationship:

\[ y = \frac{3}{2}x. \]

Next, let's analyze the options more carefully:

  1. (4, 6):

    • Calculate the ratio: \[ \frac{6}{4} = 1.5 = \frac{3}{2} \quad \text{(Valid)} \]

  2. (4, 8):

    • Calculate the ratio: \[ \frac{8}{4} = 2 \quad \text{(Not valid)} \]

  3. (6, 4):

    • Calculate the ratio: \[ \frac{4}{6} = \frac{2}{3} \quad \text{(Not valid)} \]

  4. (8, 4):

    • Calculate the ratio: \[ \frac{4}{8} = \frac{1}{2} \quad \text{(Not valid)} \]

  5. (4, 10):

    • Calculate the ratio: \[ \frac{10}{4} = 2.5 \quad \text{(Not valid)} \]

  6. (3, 8):

    • Calculate the ratio: \[ \frac{8}{3} \quad \text{(Not valid)} \]

The only pair that maintains the ratio of \( \frac{y}{x} = \frac{3}{2} \) is indeed (4, 6).

So yes, I am confident that the answer (4, 6) is correct based on the analysis of the given points and their ratios.

Use the image to answer the question.

A coordinate plane shows red paint on the X-axis and blue paint on the Y-axis. The X-axis ranges from 0 to 10 in increments of 2. The Y-axis ranges from 0 to 15 in increments of 3. The data points are left parenthesis 2 comma 3 right parenthesis, left parenthesis 4 comma 6 right parenthesis, left parenthesis 6 comma 9 right parenthesis, and left parenthesis 8 comma 12 right parenthesis.

Choose the coordinate pair to plot on the coordinate plane so the ratio stays equivalent.

(1 point)
Responses

(9, 15)
left parenthesis 9 comma 15 right parenthesis

(10, 14)
left parenthesis 10 comma 14 right parenthesis

(10, 15)
left parenthesis 10 comma 15 right parenthesis

(15, 10)
left parenthesis 15 comma 10 right parenthesis
Skip to navigation

To determine the coordinate pair that maintains the same ratio as the given points on the coordinate plane, we first identify the existing relationship between the x-values and y-values from the points provided.

The points given are:

  1. \( (2, 3) \)
  2. \( (4, 6) \)
  3. \( (6, 9) \)
  4. \( (8, 12) \)

We can observe that:

  • The x-values increase by 2: \( 2, 4, 6, 8 \)
  • The y-values increase by 3: \( 3, 6, 9, 12 \)

The ratio of y to x for these points can be summarized as:

  • For \( (2, 3) \): \(\frac{3}{2} = 1.5\)
  • For \( (4, 6) \): \(\frac{6}{4} = 1.5\)
  • For \( (6, 9) \): \(\frac{9}{6} = 1.5\)
  • For \( (8, 12) \): \(\frac{12}{8} = 1.5\)

This consistent ratio can be generalized as: \[ y = \frac{3}{2}x. \]

Now, let's check the provided options to find a pair that satisfies this ratio:

  1. (9, 15): \[ \frac{15}{9} \approx 1.67 \quad \text{(Not valid)} \]

  2. (10, 14): \[ \frac{14}{10} = 1.4 \quad \text{(Not valid)} \]

  3. (10, 15): \[ \frac{15}{10} = 1.5 \quad \text{(Valid)} \]

  4. (15, 10): \[ \frac{10}{15} \approx 0.67 \quad \text{(Not valid)} \]

Based on this analysis, the only coordinate pair that maintains the same ratio as the other points is:

(10, 15).

Use the image to answer the question.

A coordinate plane shows red paint on the X-axis and blue paint on the Y-axis. The X-axis ranges from 0 to 10 in increments of 2. The Y-axis ranges from 0 to 15 in increments of 3. The data points are left parenthesis 2 comma 3 right parenthesis, left parenthesis 4 comma 6 right parenthesis, left parenthesis 6 comma 9 right parenthesis, and left parenthesis 8 comma 12 right parenthesis.

What is the ratio of red paint to blue paint?

(1 point)
Responses

1:3
ratio of 1 to 3

1:2
ratio of 1 to 2

3:4
ratio of 3 to 4

2:3
ratio of 2 to 3
Skip to navigation

To find the ratio of red paint to blue paint from the provided data points, we will analyze the x-values (representing the red paint) and y-values (representing the blue paint) of the coordinate pairs.

The provided points are:

  1. \( (2, 3) \)
  2. \( (4, 6) \)
  3. \( (6, 9) \)
  4. \( (8, 12) \)

From these points, let's examine the relationship between the red paint (x-values) and blue paint (y-values):

  • For the first point \( (2, 3) \): \[ \text{Ratio} = \frac{2}{3} \]
  • For the second point \( (4, 6) \): \[ \text{Ratio} = \frac{4}{6} = \frac{2}{3} \]
  • For the third point \( (6, 9) \): \[ \text{Ratio} = \frac{6}{9} = \frac{2}{3} \]
  • For the fourth point \( (8, 12) \): \[ \text{Ratio} = \frac{8}{12} = \frac{2}{3} \]

The consistent ratio for red paint to blue paint from these points is \( \frac{2}{3} \).

Thus, the answer is:

2:3 (ratio of 2 to 3).

Use the image to answer the question.

A coordinate plane shows an x-axis ranging from 0 to 5 in increments of 1 and a y-axis ranging from 0 to 20 in increments of 4. The data points are left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 5 comma 20 right parenthesis.

Choose the coordinate pair to plot on the coordinate plane so the ratio stays equivalent.

(1 point)
Responses

(1, 3)
Left Parenthesis 1 comma 3 Right Parenthesis

(0, 4)
Left Parenthesis 0 comma 4 Right Parenthesis

(4, 1)
Left Parenthesis 4 comma 1 Right Parenthesis

(1, 4)
Left Parenthesis 1 comma 4 Right Parenthesis
Skip to navigation

To determine which coordinate pair to plot on the coordinate plane while maintaining the same ratio as the given points, we will analyze the existing data points to find their relationships.

The provided points are:

  1. \( (2, 8) \)
  2. \( (3, 12) \)
  3. \( (4, 16) \)
  4. \( (5, 20) \)

Calculating Ratios: Let's find the ratio of \( y \) to \( x \) for these points:

  • For the point \( (2, 8) \): \[ \frac{y}{x} = \frac{8}{2} = 4 \]

  • For the point \( (3, 12) \): \[ \frac{y}{x} = \frac{12}{3} = 4 \]

  • For the point \( (4, 16) \): \[ \frac{y}{x} = \frac{16}{4} = 4 \]

  • For the point \( (5, 20) \): \[ \frac{y}{x} = \frac{20}{5} = 4 \]

All points maintain a constant ratio of \( 4 \) or can be expressed as \( y = 4x \).

Now, we can evaluate the options provided:

  1. (1, 3): \[ \frac{3}{1} = 3 \quad \text{(Not valid since ratio is 3)} \]

  2. (0, 4): \[ \text{Undefined ratio (not valid)} \]

  3. (4, 1): \[ \frac{1}{4} = 0.25 \quad \text{(Not valid)} \]

  4. (1, 4): \[ \frac{4}{1} = 4 \quad \text{(Valid)} \]

Based on the calculation, the only coordinate pair that maintains the same ratio (\( y = 4x \)) is:

(1, 4).

Use the image to answer the question.

A coordinate plane shows an x-axis ranging from 0 to 5 in increments of 1 and a y-axis ranging from 0 to 20 in increments of 4. The data points are left parenthesis 2 comma 8 right parenthesis, left parenthesis 3 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 5 comma 20 right parenthesis.

What does the point (3, 12)
mean on this coordinate plane?

(1 point)
Responses

For every 3 of y
, 12 of another y
are needed.
For every 3 of y, 12 of another y are needed.

For every 12 of x
, 3 of y
are needed.
For every 12 of x, 3 of y are needed.

For every 3 of x
, 12 of another x
are needed.
For every 3 of x, 12 of another x are needed.

For every 3 of x
, 12 of y
are needed.
For every 3 of x, 12 of y are needed.
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page 8 of 8

In the context of the coordinate plane, the point \( (3, 12) \) represents the following:

  • The x-coordinate (3) indicates the value of \( x \) is 3.
  • The y-coordinate (12) indicates the value of \( y \) is 12.

This means that when \( x \) is 3, \( y \) is 12. It indicates a relationship between the two variables. Specifically, on this scale:

  • As you increase \( x \) by increments of 3, the corresponding increase in \( y \) is by an amount that relates to the point \( (3, 12) \).

Thus, the correct interpretation is:

For every 3 of x, 12 of y are needed.

So, the answer choice is:

For every 3 of x, 12 of y are needed.