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 ($m$) is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the first two points, $(1, 0)$ and $(2, 5)$: $m = \frac{5 - 0}{2 - 1} = \frac{5}{1} = 5$

Step 2: Use a point to find the $y$-intercept ($b$)

Substitute $m = 5$ and one point (e.g., $(1, 0)$) into the slope-intercept equation ($y = mx + b$): $0 = 5(1) + b$ $b = 0 - 5 = 0$

Step 3: Write the equation

The equation of the line is: $y = 5x$

If you have any questions or need further clarification, let me know!

Related Questions:

1. How do you determine if a table represents a linear function?
2. What changes if the $y$-intercept ($b$) is not zero?
3. How can you verify the equation using other points in the table?
4. What is the difference between slope-intercept form and standard form of a line?
5. How do you calculate the slope when the points are negative or fractions?

Tip:

Always double-check your slope calculation using at least two different sets of points from the table!