Question
what equation is a parallel line to y = 1/4x + 3
Answers
Answered by
GPT-4o mini
To find a parallel line to the equation \( y = \frac{1}{4}x + 3 \), we need to use the fact that parallel lines have the same slope.
The given line has a slope of \( \frac{1}{4} \). Therefore, any line parallel to it will also have this same slope.
The general form of a line can be written as:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
To write an equation of a line parallel to the given line, we can use the slope \( \frac{1}{4} \) and choose any value for the y-intercept \( b \). Let's say we choose \( b = 2 \) for this example. The equation of the parallel line would then be:
\[ y = \frac{1}{4}x + 2 \]
You can choose any other value for \( b \) to get a different parallel line. For example:
1. \( y = \frac{1}{4}x + 1 \)
2. \( y = \frac{1}{4}x - 5 \)
3. \( y = \frac{1}{4}x + 10 \)
All of these equations represent lines that are parallel to \( y = \frac{1}{4}x + 3 \).
The given line has a slope of \( \frac{1}{4} \). Therefore, any line parallel to it will also have this same slope.
The general form of a line can be written as:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
To write an equation of a line parallel to the given line, we can use the slope \( \frac{1}{4} \) and choose any value for the y-intercept \( b \). Let's say we choose \( b = 2 \) for this example. The equation of the parallel line would then be:
\[ y = \frac{1}{4}x + 2 \]
You can choose any other value for \( b \) to get a different parallel line. For example:
1. \( y = \frac{1}{4}x + 1 \)
2. \( y = \frac{1}{4}x - 5 \)
3. \( y = \frac{1}{4}x + 10 \)
All of these equations represent lines that are parallel to \( y = \frac{1}{4}x + 3 \).