Questions: Consider the line y=2/5 x. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: Slope of a perpendicular line:

Solution Steps

To find the slope of a line parallel to a given line, we use the fact that parallel lines have the same slope. Therefore, the slope of a line parallel to \( y = \frac{2}{5}x \) is also \(\frac{2}{5}\).

To find the slope of a line perpendicular to a given line, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Therefore, the slope of a line perpendicular to \( y = \frac{2}{5}x \) is \(-\frac{5}{2}\).

The equation of the line is given as \( y = \frac{2}{5}x \). The slope of this line is the coefficient of \( x \), which is \( \frac{2}{5} \).

Lines that are parallel have the same slope. Therefore, the slope of a line parallel to the given line is also \( \frac{2}{5} \).

The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. The negative reciprocal of \( \frac{2}{5} \) is calculated as follows: \[ \text{Slope of perpendicular line} = -\frac{1}{\left(\frac{2}{5}\right)} = -\frac{5}{2} \]

Final Answer