Let's examine the two given functions: [tex]\( y = 3x + 4 \)[/tex] and [tex]\( y = 5x + 4 \)[/tex].
### Understanding the Components:
A linear equation in the form [tex]\( y = mx + b \)[/tex] has two primary components:
1. [tex]\( m \)[/tex] (the slope): Determines the steepness or incline of the line.
2. [tex]\( b \)[/tex] (the y-intercept): Indicates where the line crosses the y-axis.
### Comparing Slopes:
- The slope of the first function, [tex]\( y = 3x + 4 \)[/tex], is [tex]\( m = 3 \)[/tex].
- The slope of the second function, [tex]\( y = 5x + 4 \)[/tex], is [tex]\( m = 5 \)[/tex].
### Analyzing the Slopes:
- A greater slope value means the line is steeper.
- In this case, the slope changes from 3 to 5. Since 5 is greater than 3, the new line ([tex]\( y = 5x + 4 \)[/tex]) will be steeper compared to the original line ([tex]\( y = 3x + 4 \)[/tex]).
### Checking the Intercepts:
- Both functions have the same y-intercept (4). Thus, there is no vertical shift in the y-axis.
### Conclusion:
The change in the slope from 3 to 5 makes the line steeper.
Therefore, the correct answer is:
B. It would be steeper.
