Linear Function Table: Match Values (0,5), (1,6), (2,7) to Its Equation

Below is a table containing values for x and y. This tables represents a linear function.

Choose the equation that corresponds to the function.

To solve this problem, we'll proceed with the following steps:

• Step 1: Find the slope $m$.
• Step 2: Use the slope and a point to find the $y$-intercept $b$.
• Step 3: Write the linear equation.

Let's work through each step:

Step 1: Calculate the slope $m$.
Using the points $(0, 5)$ and $(1, 6)$, the slope $m$ is calculated as follows:

$m = \frac{6 - 5}{1 - 0} = \frac{1}{1} = 1$

Step 2: Use the slope ($m = 1$) to find the $y$-intercept $b$.
We know from the point $(0, 5)$ that when $x = 0$, $y = 5$, which directly gives us the $y$-intercept:

$b = 5$

Step 3: Form the equation of the line using $y = mx + b$.
Substitute the found values into the equation:

$y = 1 \cdot x + 5$

Simplifying gives:

$y = x + 5$

Thus, the equation corresponding to the function is $y = x + 5$.