Questions: Identifying linear functions given ordered pairs For each function, state whether it is linear.

Transcript text: Identifying linear functions given ordered pairs For each function, state whether it is linear.

Solution

Solution Steps

To determine whether a function is linear given ordered pairs, we need to check if the rate of change between the pairs is constant. A linear function has a constant slope, which means the difference in the \(y\)-values divided by the difference in the \(x\)-values (the slope) should be the same for all pairs.

Step 1: Identify the Ordered Pairs

Assume we have a set of ordered pairs: \((x_1, y_1), (x_2, y_2), (x_3, y_3), \ldots\).

Step 2: Calculate the Slope Between Each Pair

For each consecutive pair of points, calculate the slope using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Repeat this calculation for each pair of consecutive points.

Step 3: Check for Consistency

Compare the slopes calculated in Step 2. If all the slopes are equal, the function is linear. If any slope differs, the function is not linear.