The two tables of data represent relationships between x and y. Graph the relationship that is proportional.

Question

x y
1 2.5
3 7.5
8 20
x y
1 3
2 10
4 24

Answer 1

To determine which of the two sets of data represents a proportional relationship, we need to check whether the ratio of \( y \) to \( x \) is constant.

First Table:

Let's examine the first table:

\[ \begin{array}{|c|c|} \hline x & y \ \hline 1 & 2.5 \ 3 & 7.5 \ 8 & 20 \ \hline \end{array} \]

Calculating the ratio \( \frac{y}{x} \):

• For \( x = 1 \), \( \frac{y}{x} = \frac{2.5}{1} = 2.5 \)
• For \( x = 3 \), \( \frac{y}{x} = \frac{7.5}{3} = 2.5 \)
• For \( x = 8 \), \( \frac{y}{x} = \frac{20}{8} = 2.5 \)

Since the ratio \( \frac{y}{x} = 2.5 \) is constant for all points, the first table represents a proportional relationship.

Second Table:

Now let's look at the second table:

\[ \begin{array}{|c|c|} \hline x & y \ \hline 1 & 3 \ 2 & 10 \ 4 & 24 \ \hline \end{array} \]

Calculating the ratio \( \frac{y}{x} \):

• For \( x = 1 \), \( \frac{y}{x} = \frac{3}{1} = 3 \)
• For \( x = 2 \), \( \frac{y}{x} = \frac{10}{2} = 5 \)
• For \( x = 4 \), \( \frac{y}{x} = \frac{24}{4} = 6 \)

Since the ratios are different, \( 3 \), \( 5 \), and \( 6 \), this table does not represent a proportional relationship.

Conclusion:

The first table represents a proportional relationship given that \( \frac{y}{x} \) remains constant at \( 2.5 \).

Graph of the First Table:

To graph the relationship from the first table, you would plot the points:

• \( (1, 2.5) \)
• \( (3, 7.5) \)
• \( (8, 20) \)

The line through these points will have a slope equal to the constant ratio \( 2.5 \), indicating a proportional relationship.

When you plot it, you'll see a straight line that passes through the origin (0,0), confirming it is a proportional relationship.

Answer 2

what spots should I plot

Answer 3

To plot the points from the first table that represents a proportional relationship, you'll use the following coordinates:

1. \( (1, 2.5) \)
2. \( (3, 7.5) \)
3. \( (8, 20) \)

Steps to Plot:

1. Set Up Your Axes:

   • Draw a horizontal axis (x-axis) and a vertical axis (y-axis).
   • Label your x-axis with values (consider setting up at least from \( 0 \) to \( 10 \) or higher, as needed).
   • Label your y-axis with values (consider ranging from \( 0 \) to \( 25 \) or higher to accommodate the y-values).

2. Plot the Points:

   • For \( (1, 2.5) \):
     • Move to \( x = 1 \) on the x-axis, then go up to \( y = 2.5 \) (this is halfway between 2 and 3).
     • Mark this point.
   • For \( (3, 7.5) \):
     • Move to \( x = 3 \) on the x-axis, then go up to \( y = 7.5 \) (this is halfway between 7 and 8).
     • Mark this point.
   • For \( (8, 20) \):
     • Move to \( x = 8 \) on the x-axis, then go up to \( y = 20 \).
     • Mark this point.

3. Draw the Line:

   • After plotting the points, draw a straight line through them. Since this is a proportional relationship, the line should pass through the origin (0, 0) and extend through the plotted points.

Summary of Points to Plot:

• \( (1, 2.5) \)
• \( (3, 7.5) \)
• \( (8, 20) \)

This will illustrate the linear relationship between \( x \) and \( y \) described in your first table.