Question

The coordinate (1/2,1) is on the graph of the proportional relationship identify another point on the graph

Answer 1

Options
(2/3, 4)
(2, 6)
(3/2, 3)
(1/4, 2)

Answer 2

A proportional relationship can be represented by the equation \( y = kx \), where \( k \) is the constant of proportionality. If the point \((\frac{1}{2}, 1)\) is on the graph, we can find \( k \) by substituting the coordinates into the equation.

\[
1 = k \cdot \frac{1}{2}
\]

To find \( k \), we can solve for \( k \):

\[
k = 1 \div \frac{1}{2} = 2
\]

Now that we know the constant of proportionality \( k \) is 2, we can write the equation of the proportional relationship as:

\[
y = 2x
\]

To find another point on this graph, you can choose any value for \( x \) and then calculate \( y \). For example, let’s use \( x = 1 \):

\[
y = 2(1) = 2
\]

Thus, another point on the graph is \( (1, 2) \).

You can also find other points by selecting different \( x \) values. For instance:

- If \( x = 0 \), then \( y = 2(0) = 0 \) → Point \( (0, 0) \).
- If \( x = 2 \), then \( y = 2(2) = 4 \) → Point \( (2, 4) \).

Any of these points are valid points on the graph of the proportional relationship defined by \( y = 2x \).

Answer 3

To determine which of the given options is on the graph of the proportional relationship \( y = 2x \), we can substitute the \( x \)-coordinate of each point into the equation and see if it yields the corresponding \( y \)-coordinate.

1. **For (2/3, 4)**:
\[
y = 2\left(\frac{2}{3}\right) = \frac{4}{3} \quad \text{(not equal to 4)}
\]

2. **For (2, 6)**:
\[
y = 2(2) = 4 \quad \text{(not equal to 6)}
\]

3. **For (3/2, 3)**:
\[
y = 2\left(\frac{3}{2}\right) = 3 \quad \text{(equal to 3)}
\]

4. **For (1/4, 2)**:
\[
y = 2\left(\frac{1}{4}\right) = \frac{2}{4} = \frac{1}{2} \quad \text{(not equal to 2)}
\]

The only point that satisfies the equation \( y = 2x \) from the options given is **(3/2, 3)**.