Given a table of values for a linear relationship, what is the correct method to find the slope of the line?

• A. Multiply all y-values together and divide by the sum of all x-values
• B. Add all x-values and y-values, then divide the total y by the total x
• C. Calculate the change in y divided by the change in x between any two points: m = (y_2 - y_1) / (x_2 - x_1)
• D. Subtract the smallest x-value from the largest y-value

Answer: (C)

Verified step by step guidance

1. Identify two distinct points from the table, each with coordinates \((x_1, y_1)\) and \((x_2, y_2)\).
2. Calculate the difference in the y-values between these two points: \(\Delta y = y_2 - y_1\).
3. Calculate the difference in the x-values between these two points: \(\Delta x = x_2 - x_1\).
4. Use the formula for the slope of a line, which is the ratio of the change in y to the change in x: \(m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}\).
5. Interpret the slope \(m\) as the rate at which y changes for each unit change in x, confirming the linear relationship.