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?
A. The line shifts up.
B. The line shifts down.
C. The line is more steep.
D. The line is less steep.
Changing the y-intercept of the function does not affect the steepness of the line. However, it does affect the vertical position of the line. If the y-intercept is changed to a smaller positive number, it means the line will intersect the y-axis at a lower point. This indicates that the line shifts down.
Therefore, the correct answer is B. The line shifts down.
To determine the effect on the graph of the function if the y-intercept is changed to a smaller positive number, we need to understand the concept of the y-intercept.
The y-intercept is the point at which the graph of a function intersects the y-axis. It is the value of y when x is equal to 0.
In the given function, y = 8 - 2x, the y-intercept is 8.
If the y-intercept is changed to a smaller positive number, that means the y-value of the point where the graph intersects the y-axis will decrease.
Therefore, the correct answer is B. The line shifts down.
To determine the effect on the graph of the given function if the y-intercept is changed to a smaller positive number, we need to understand the relationship between the y-intercept and the position of the graph.
The y-intercept is the value of y when x is equal to 0. In the given function, y = 8 - 2x, the y-intercept is 8.
If the y-intercept is changed to a smaller positive number, it means the value of y when x is equal to 0 will be smaller than 8.
To visualize this, let's take two scenarios:
Scenario 1: y-intercept is 8
In this case, when x is equal to 0, y = 8. This gives us the point (0, 8) on the graph.
Scenario 2: y-intercept is a smaller positive number, let's say 4
In this case, when x is equal to 0, y = 4. This gives us the point (0, 4) on the graph.
Comparing the two scenarios, we can see that the graph shifts down because the y-coordinate of the y-intercept is smaller in Scenario 2 (4) compared to Scenario 1 (8). Therefore, the correct answer is option B: The line shifts down.