To answer this question, we need to compare the two linear equations and understand their characteristics, specifically focusing on the slope, since the slope determines the steepness of the line.
The first equation given is:
[tex]\[ y = 5x - 2 \][/tex]
Here, the slope (m1) is 5.
The second equation given is:
[tex]\[ y = \frac{3}{4}x - 2 \][/tex]
Here, the slope (m2) is [tex]\(\frac{3}{4}\)[/tex].
Comparing the slopes of both lines:
- The slope of the first line (5) is greater than the slope of the second line ([tex]\(\frac{3}{4}\)[/tex]).
When comparing two slopes:
- A greater slope indicates a steeper line.
- A smaller slope indicates a less steep line.
Since 5 is greater than [tex]\(\frac{3}{4}\)[/tex], the line with the slope of [tex]\(\frac{3}{4}\)[/tex] is less steep than the line with the slope of 5.
Therefore, the graph of the new function [tex]\( y = \frac{3}{4}x - 2 \)[/tex] would be less steep compared to the graph of the original function [tex]\( y = 5x - 2 \)[/tex].
Thus, the correct answer is:
B. It would be less steep.
