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