To find the equation of the linear function in slope-intercept form $y = mx + b$, follow these steps:

Step 1: Identify Two Points

From the table, we have the points: $(-2, 6), \quad (3, -4), \quad (8, -14), \quad (13, -24)$

Step 2: Calculate the Slope $m$

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(-2,6)$ and $(3,-4)$:

$m = \frac{-4 - 6}{3 - (-2)} = \frac{-10}{5} = -2$

Step 3: Find the y-Intercept $b$

Using the slope-intercept form $y = mx + b$ and one of the points, say $(-2,6)$:

$6 = (-2)(-2) + b$

$6 = 4 + b$

$b = 2$

Step 4: Write the Final Equation

$y = -2x + 2$

Thus, the equation of the linear function is: $\boxed{y = -2x + 2}$

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Related Questions

1. How do you determine if a function is linear from a table?
2. What happens when the slope of a linear equation is negative?
3. How can you find the equation of a line given any two points?
4. What is the significance of the y-intercept in a real-world scenario?
5. How do parallel and perpendicular slopes relate?

Tip:

To verify your equation, substitute other points from the table into $y = -2x + 2$ and check if they satisfy the equation!