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To find the equation of the linear function represented by the table in slope-intercept form (\(y = mx + b\)):

### Step 1: Calculate the slope (\(m\)):
The slope is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
From the table, let’s use two points, \((1, 1)\) and \((5, 15)\):
\[
m = \frac{15 - 1}{5 - 1} = \frac{14}{4} = 3.5
\]

### Step 2: Find the y-intercept (\(b\)):
Using the slope (\(m = 3.5\)) and one of the points, say \((1, 1)\), substitute into the slope-intercept form:
\[
y = mx + b
\]
\[
1 = 3.5(1) + b
\]
\[
b = 1 - 3.5 = -2.5
\]

### Step 3: Write the equation:
The equation of the linear function is:
\[
y = 3.5x - 2.5
\]

Would you like further clarification or verification? 

### Questions to expand on:
1. What is the significance of the slope and y-intercept in the equation of a line?
2. How can you verify the equation by using the other points in the table?
3. What changes in the equation if the slope is negative?
4. Can you use a graph to confirm this equation?
5. How would you rewrite this equation in standard form?

**Tip:** Always double-check your calculations by substit

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

Learn how to derive the equation of a linear function from a given table in slope-intercept form. This step-by-step solution includes calculating the slope and determining the y-intercept. Suitable for students in Grades 8-10.

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