Consider the function: y = 8 − 2x.
What is the effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number?
Responses
A The line shifts up.The line shifts up.
B The line shifts down.The line shifts down.
C The line is more steep.The line is more steep.
D The line is less steep.
B The line shifts down.
B The line shifts down.
To determine the effect on the graph of the function, we need to understand what the y-intercept represents.
The y-intercept is the point where the graph intersects the y-axis. In the given function y = 8 - 2x, the y-intercept is the value of y when x is equal to 0.
If the y-intercept is changed to a smaller positive number, it means that the y-coordinate of the point where the graph intersects the y-axis will decrease.
Since the y-coordinate of any point on the graph is given by the equation y = 8 - 2x, changing the y-intercept will result in a downward shift of the entire graph.
Therefore, the correct answer is:
B) The line shifts down.