Equations in Tables: Matching Functions with Data Values

Which of the following equations corresponds to the function represented in the table?

To solve this problem, we'll follow these steps:

• Step 1: Determine the form of the potential equation.
• Step 2: Calculate the slope using two points from the table.
• Step 3: Identify the y-intercept.

Now, let's work through each step:

Step 1: Determine the Equation Form
Since the relationship appears linear, we'll use $y = mx + b$.

Step 2: Calculate the Slope
Using the points $(-1, 1)$ and $(0, 2)$, calculate the slope:
$m = \frac{2 - 1}{0 - (-1)} = \frac{1}{1} = 1$.

Step 3: Identify the Y-Intercept
Using the slope $m = 1$ and point $(0, 2)$, since the y-intercept $b$ is the $y$-value when $x = 0$, $b = 2$.

Thus, the equation is $y = x + 2$.

Verify by checking all points from the table:
- For $X = -1, Y = 1$: $1 = -1 + 2$
- For $X = 0, Y = 2$: $2 = 0 + 2$
- For $X = 1, Y = 3$: $3 = 1 + 2$
- For $X = 2, Y = 4$: $4 = 2 + 2$
- For $X = 3, Y = 5$: $5 = 3 + 2$

Thus the equation $y = x + 2$ satisfies all table values.

Therefore, the solution to the problem is $y = x + 2$.