Questions: If the slope m of the graph of a linear function is square , the function is increasing over its domain.

Transcript text: If the slope $m$ of the graph of a linear function is $\square$ , the function is increasing over its domain.

Solution

Solution Steps

To determine when a linear function is increasing, we need to consider the slope $ m $ of the function. A linear function is increasing over its domain if its slope $ m $ is positive. Therefore, the blank should be filled with "positive."

Step 1: Understanding the Condition for an Increasing Function

A linear function is represented by the equation $ y = mx + b $, where $ m $ is the slope. The function is increasing over its domain if the slope $ m $ is positive. This means that as $ x $ increases, $ y $ also increases.

Step 2: Analyzing the Given Slope

In the given scenario, the slope $ m $ is $ 2 $. Since $ 2 > 0 $, the condition for the function to be increasing is satisfied.

Final Answer

The function is increasing if the slope $ m $ is positive. For the given slope $ m = 2 $, the function is indeed increasing. Therefore, the answer is $\boxed{\text{positive}}$.

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