We are given a table of x and y values that represent a linear function. We need to determine the equation of this linear function in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Problem Description

We are given a table of x and y values that represent a linear function. We need to determine the equation of this linear function in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Solution Steps

First, we need to determine the slope $m$. We can use any two points from the table to calculate the slope. Let's use the points $(-6, 64)$ and $(-3, 31)$. The formula for the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Plugging in the coordinates of the points, we get:

$m = \frac{31 - 64}{-3 - (-6)} = \frac{-33}{3} = -11$

So, the slope $m = -11$.

Now, we need to find the y-intercept $b$. We can use the slope-intercept form and substitute the slope and one of the points from the table to solve for $b$. Let's use the point $(-1, 9)$.

$y = mx + b$

$9 = (-11)(-1) + b$

$9 = 11 + b$

$b = 9 - 11$

$b = -2$

Therefore, the y-intercept is $b = -2$.

The y-intercept as an ordered pair is $(0, -2)$.

Now that we have the slope $m = -11$ and the y-intercept $b = -2$, we can write the equation of the linear function in slope-intercept form:

$y = -11x - 2$

3. Final Answer

Slope: -11

Vertical Intercept (as an ordered pair): (0, -2)

Equation for the Linear Function: $y = -11x - 2$