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If [tex][tex]$y = 3x + 4$[/tex][/tex] were changed to [tex][tex]$y = 5x + 4$[/tex][/tex], how would the graph of the new function compare with the first one?

A. It would be less steep.
B. It would be steeper.
C. It would be shifted right.
D. It would be shifted up.

Sagot :

GinnyAnswer
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.
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