1. **Stating the problem:** We are investigating how the slope $m$ of a line affects the graph of the line as $m$ changes. 2. **Formula used:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Important rules about slope:** - If $m > 0$, the line slopes upward (positive slope). - If $m < 0$, the line slopes downward (negative slope). - If $m = 0$, the line is horizontal. - The larger the absolute value of $m$, the steeper the line. 4. **As $m$ changes from 1 to 3:** - Since $m$ is positive and increasing, the line becomes steeper. - The graph moves upward more sharply as $x$ increases. 5. **As $m$ changes from -6 to -1:** - Since $m$ is negative but increasing towards zero, the line becomes less steep (closer to horizontal). - The graph still slopes downward but less sharply. 6. **If $m$ is negative:** - The slope of the line is negative, meaning the line slopes downward from left to right. **Final answers:** - As $m$ changes from 1 to 3, the graph **gets steeper**. - As $m$ changes from -6 to -1, the graph **gets less steep**. - If $m$ is negative, the slope of the line is **negative**.