Given a line with a slope of 4, how does the graph of the line differ if the slope is changed to -4?
a) There is no change
b) It moves 8 units in the y axis
c) It moves 8 units on the x axis
d) It changes from uphill to downhill
e) It changes from downhill to uphill
To understand how the graph of a line changes when the slope is changed, let's start by understanding what the slope represents. The slope of a line describes how steeply it rises or falls as we move from left to right.
Given a line with a slope of 4, it means that for every 1 unit moved horizontally to the right, the line moves 4 units vertically upward. In other words, the line has a positive slope and moves uphill.
Now, if we change the slope to -4, it means that for every 1 unit moved horizontally to the right, the line moves 4 units vertically downward. This corresponds to a negative slope and the line will move downhill.
Therefore, the correct answer is:
d) It changes from uphill to downhill