To find the equation of the linear function represented by the table, we need to follow these steps:

1. Determine the slope (m): The slope of a linear function is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's take two points from the table:

   • Point 1: $(-1, 0)$
   • Point 2: $(1, -4)$

   Using the slope formula: $m = \frac{-4 - 0}{1 - (-1)} = \frac{-4}{2} = -2$ So, the slope $m = -2$.

2. Find the y-intercept (b): We will use the slope-intercept form of a linear equation: $y = mx + b$ Now, substitute one of the points into this equation to solve for $b$. Using the point $(-1, 0)$: $0 = -2(-1) + b$ $0 = 2 + b$ $b = -2$

3. Write the equation: Now that we have the slope $m = -2$ and the y-intercept $b = -2$, the equation of the line is: $y = -2x - 2$

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to explore:

1. How do you find the slope from two points on a line?
2. How do changes in the slope affect the steepness of the graph?
3. What does the y-intercept represent on a graph?
4. How can you verify if a set of points lies on a specific line?
5. How would the equation change if the line had a positive slope?

Tip: Always verify your calculated equation by substituting points from the table back into the equation to check for consistency.