Find the equation of the linear function represented by the table below in slope-intercept form.
x	y
minus, 2−2	66
33	minus, 4−4
88	minus, 14−14
1313	minus, 24−24


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!

Find the equation of the linear function represented by the table below in slope-intercept form.

x    y
-2   6
3    -4
8    -14
13   -24

Learn how to find the equation of a linear function represented by a table of values. This step-by-step guide explains slope calculation, finding the y-intercept, and writing the equation in slope-intercept form, using points like (-2, 6) and (3, -4). Suitable for students in Grades 8-10.

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