Question

the table shows the values of x and y: x values are 2, 0, 1, -1, 1/3, 1.5; y values are 7, 1, 4, -2, 2, 5.5

Explanation:

Since the problem is not clearly stated, I assume we need to find the relationship between \(x\) and \(y\) (like the function rule). Let's check the pattern:

Step1: Assume linear function \(y = ax + b\)

Take two points, e.g., \(x = 0\), \(y = 1\) (so \(b = 1\)). Then take \(x = 1\), \(y = 4\): \(4 = a(1)+1\) → \(a = 3\). Check another point: \(x = -1\), \(y = -2\). \(y = 3(-1)+1=-2\), which matches. Check \(x = 2\): \(3(2)+1 = 7\), matches. \(x=\frac{1}{3}\): \(3(\frac{1}{3})+1 = 2\), matches. \(x = 1.5\): \(3(1.5)+1 = 5.5\), matches.

Step2: Confirm the function

The function is \(y = 3x + 1\).

Answer:

The relationship between \(x\) and \(y\) is \(y = 3x + 1\) (if the problem was to find the function; adjust based on actual question).