Answer :
To determine the slope of a line that is parallel to the line given by the equation \( y = \frac{1}{2}x + 3 \), we need to understand a few key concepts about linear equations and parallel lines.
1. Slope-Intercept Form: The equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
where \( m \) represents the slope of the line and \( b \) represents the y-intercept.
2. Identifying the Slope: In the equation of the given line \( y = \frac{1}{2}x + 3 \), the slope \( m \) is the coefficient of \( x \). Therefore, the slope of the given line is:
[tex]\[ m = \frac{1}{2} \][/tex]
3. Parallel Lines and Slope: Parallel lines have identical slopes. This means that any line that is parallel to the original line will have the same slope as the original line.
4. Conclusion: Since the slope of the original line \( y = \frac{1}{2}x + 3 \) is \( \frac{1}{2} \), any line parallel to it will also have a slope of \( \frac{1}{2} \).
Therefore, the slope of a line that is parallel to \( y = \frac{1}{2}x + 3 \) is:
[tex]\[ \boxed{0.5} \][/tex]
1. Slope-Intercept Form: The equation of a line in slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
where \( m \) represents the slope of the line and \( b \) represents the y-intercept.
2. Identifying the Slope: In the equation of the given line \( y = \frac{1}{2}x + 3 \), the slope \( m \) is the coefficient of \( x \). Therefore, the slope of the given line is:
[tex]\[ m = \frac{1}{2} \][/tex]
3. Parallel Lines and Slope: Parallel lines have identical slopes. This means that any line that is parallel to the original line will have the same slope as the original line.
4. Conclusion: Since the slope of the original line \( y = \frac{1}{2}x + 3 \) is \( \frac{1}{2} \), any line parallel to it will also have a slope of \( \frac{1}{2} \).
Therefore, the slope of a line that is parallel to \( y = \frac{1}{2}x + 3 \) is:
[tex]\[ \boxed{0.5} \][/tex]
