Consider the function: y = 8 - 2x.
What is the effect on the graph for the given function if the slope of the function is changed to -10?
A. The line shifts up.
B. The line shifts down.
C. The line is more steep.
D. The line is less steep.
C. The line is more steep.
The correct answer is D. The line is less steep.
The slope of the function determines the steepness of the line. In the given function y = 8 - 2x, the slope is -2. When the slope is changed to -10, the line becomes less steep. A larger magnitude for the slope corresponds to a steeper line, while a smaller magnitude corresponds to a less steep line.
To determine the effect on the graph of the function when the slope is changed, we need to understand how the slope affects the line.
The slope of a linear function determines how steep the line is. If the slope is positive, the line will slant upward from left to right. If the slope is negative, the line will slant downward from left to right. The larger the absolute value of the slope, the steeper the line.
In the given function y = 8 - 2x, the slope is -2.
If the slope is changed to -10, the line will become steeper because the absolute value of the slope has increased. Since -10 is larger than -2, the line will slant more downward from left to right.
Therefore, the correct answer is:
C. The line is more steep.