Question

Which equation represents the relationship shown in the table?

x 1 5 7
y 4 20 28
Responses

y=x4
y equals x over 4

y=4x
y equals 4 x

y=x+3
y equals x plus 3

x=y−15
x equals y minus 15

Answer 1

To determine the equation that represents the relationship shown in the table, we can analyze the given values of \(x\) and \(y\).

The table provides the following pairs:

- When \(x = 1\), \(y = 4\)
- When \(x = 5\), \(y = 20\)
- When \(x = 7\), \(y = 28\)

Now, let's check which of the given equations fits the data:

1. **Check \(y = \frac{x}{4}\)**:
- For \(x = 1\), \(y = \frac{1}{4} = 0.25\) (not a match)

2. **Check \(y = 4x\)**:
- For \(x = 1\), \(y = 4(1) = 4\) (match)
- For \(x = 5\), \(y = 4(5) = 20\) (match)
- For \(x = 7\), \(y = 4(7) = 28\) (match)

Since all the values match, this equation holds true for all cases.

3. **Check \(y = x + 3\)**:
- For \(x = 1\), \(y = 1 + 3 = 4\) (match)
- For \(x = 5\), \(y = 5 + 3 = 8\) (not a match)
- (No need to check further; fails)

4. **Check \(x = y - 15\)**:
- For \(x = 1\), \(1 = y - 15\) → \(y = 16\) (not a match)

The only equation that fits all provided points is \(y = 4x\).

Thus, the correct relationship is:

**y = 4x**