Linear Function: Find the Equation from Table Values (2,13) to (-1,4)

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 determine the equation of the linear function from the given table, we'll follow these steps:

• Step 1: Calculate the Slope ($m$)
• Step 2: Find the Y-intercept ($b$)
• Step 3: Formulate the Linear Equation

Let's delve into each step:

Step 1: Calculate the Slope ($m$)
Using two points from the table, $(2, 13)$ and $(1, 10)$, we calculate the slope $m$ using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 13}{1 - 2} = \frac{-3}{-1} = 3$

Thus, the slope $m$ is 3.

Step 2: Find the Y-intercept ($b$)
The y-intercept $b$ is easily found because it is where $x = 0$. From the table, when $x = 0$, $y = 7$, therefore $b = 7$.

Step 3: Formulate the Linear Equation
Substitute the values of $m$ and $b$ into the linear equation format:

$y = 3x + 7$

Hence, the equation that represents the linear function is $y = 3x + 7$.

Checking against the provided choices, the equation corresponds to choice 2.