Question
Which characteristics of nonvertical lines that make slope-intercept form (y = mx + b) a good choice when writing an equation for this type of line.
Which characteristics of nonvertical lines that make slope-intercept form (y = mx + b) a good choice when writing an equation for this type of line.
They all have a constant rate of change.
They all cross the y-axis.
They all have positive slopes.
They all have negative slopes.
They all cross the y-axis at 0.
Which characteristics of nonvertical lines that make slope-intercept form (y = mx + b) a good choice when writing an equation for this type of line.
They all have a constant rate of change.
They all cross the y-axis.
They all have positive slopes.
They all have negative slopes.
They all cross the y-axis at 0.
Answers
Answered by
GPT-4o mini
The characteristics of nonvertical lines that make slope-intercept form \( y = mx + b \) a good choice when writing an equation for this type of line include:
1. **They all have a constant rate of change.**
- This is a key characteristic of linear functions. The slope \( m \) in the equation represents this constant rate of change.
2. **They all cross the y-axis.**
- The \( b \) in the slope-intercept form represents the y-intercept, which is the point where the line crosses the y-axis. This is true for all nonvertical lines.
The other statements are not universally true for all nonvertical lines:
- **They all have positive slopes.**
- This is not true; nonvertical lines can have either positive or negative slopes.
- **They all have negative slopes.**
- Like the previous statement, this is not universally true; nonvertical lines can have either positive or negative slopes.
- **They all cross the y-axis at 0.**
- This is only true for a specific case where the y-intercept \( b = 0 \). Nonvertical lines can cross the y-axis at any point.
In summary, the two key characteristics that make slope-intercept form a good choice for nonvertical lines are the constant rate of change and the fact that they all cross the y-axis.
1. **They all have a constant rate of change.**
- This is a key characteristic of linear functions. The slope \( m \) in the equation represents this constant rate of change.
2. **They all cross the y-axis.**
- The \( b \) in the slope-intercept form represents the y-intercept, which is the point where the line crosses the y-axis. This is true for all nonvertical lines.
The other statements are not universally true for all nonvertical lines:
- **They all have positive slopes.**
- This is not true; nonvertical lines can have either positive or negative slopes.
- **They all have negative slopes.**
- Like the previous statement, this is not universally true; nonvertical lines can have either positive or negative slopes.
- **They all cross the y-axis at 0.**
- This is only true for a specific case where the y-intercept \( b = 0 \). Nonvertical lines can cross the y-axis at any point.
In summary, the two key characteristics that make slope-intercept form a good choice for nonvertical lines are the constant rate of change and the fact that they all cross the y-axis.
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