Final answer:
Increasing the slope of a linear function from 2 to 8 causes the graph to become steeper because a steeper slope indicates a steeper incline on the graph.
Step-by-step explanation:
Changing the slope of a linear function from 2 to 8 causes the graph to become steeper. This is because the slope of a line represents its steepness or the rate at which the line rises or falls. A higher positive slope indicates a steeper incline going upwards, and conversely, a smaller positive slope gives a flatter incline. Therefore, increasing the slope from 2 to 8 would result in a steeper upward tilt to the line.
If we consider lines with negative slopes, a larger absolute value of the slope will still imply a steeper line but in the downward direction. A vertical shift, on the other hand, happens only when the y-intercept is altered. This causes the line to move up or down on the graph, maintaining the same slope. Thus, increasing the slope causes the graph to steepen, not shift vertically.