Consider the function y=8-2x. It hat 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. Line shifts up b. Line shifts down c. Line is more steep d. Line is less steep
The given function is y = 8-2x, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
The y-intercept of the function is 8, which means the graph intersects the y-axis at the point (0, 8).
If the y-intercept is changed to a smaller positive number a, it means the graph would intersect the y-axis at the point (0, a).
- This would result in the line shifting up if a is greater than 8, or
- Line shifting down if a is smaller than 8.
Therefore, the correct answer is: b. Line shifts down.
To determine the effect on the graph of the function y = 8 - 2x when the y-intercept is changed to a smaller positive number, we need to understand the impact of changing the value of the y-intercept.
The y-intercept is the point where the graph intersects the y-axis. In this case, the original function has a y-intercept of 8, meaning it crosses the y-axis at the point (0, 8). When we change the y-intercept to a smaller positive number a, let's say (0, a), the graph will shift either up or down depending on the value of a.
Now, let's consider the given options:
a. Line shifts up: If the y-intercept is changed to a smaller positive number a, the line will shift up, as the new y-intercept will be at a higher y-value compared to the original y-intercept of 8. The line will become steeper in this case.
b. Line shifts down: If the y-intercept is changed to a smaller positive number a, the line will shift down, as the new y-intercept will be at a lower y-value compared to the original y-intercept of 8. The line will become less steep in this case.
c. Line is more steep: Changing the y-intercept to a smaller positive number will not affect the slope of the line (which is -2 in this case), so the line will not become steeper.
d. Line is less steep: Changing the y-intercept to a smaller positive number will not affect the slope of the line (which is -2 in this case), so the line will not become less steep.
Therefore, the correct answer is either a. Line shifts up or b. Line shifts down, depending on whether the new y-intercept (0, a) is higher or lower than the original y-intercept at (0, 8).
The given function is y = 8 - 2x.
The y-intercept of the function represents the value of y when x is equal to 0. If the y-intercept is changed to a smaller positive number a, it means that the value of y when x is equal to 0 is smaller.
To understand the effect on the graph, let's consider the original function and the modified function with the new y-intercept a:
Original function: y = 8 - 2x
Modified function: y = a - 2x
a) Line shifts up: If the y-intercept is changed to a smaller positive number, the line shifts up. However, in this case, since we are changing the y-intercept to a smaller positive number, the line actually shifts down.
b) Line shifts down: This is the correct answer. If the y-intercept is changed to a smaller positive number, the line will shift down.
c) Line is more steep: The steepness of a line is determined by the slope, which is -2 in this case. Changing the y-intercept does not affect the steepness of the line, so the line will have the same slope as before.
d) Line is less steep: Same as answer c, the steepness (slope) of the line remains the same.
Therefore, the correct answer is b) Line shifts down.