consider the line $y = \\frac{1}{5}-\\frac{3}{2}x$. what is the slope of a line parallel to this line? what…

Explanation:

Step1: Recall slope - parallel line relationship

Parallel lines have equal slopes. The given line is in slope - intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the line $y=\frac{1}{5}-\frac{3}{2}x$, or $y =-\frac{3}{2}x+\frac{1}{5}$, the slope $m =-\frac{3}{2}$. So the slope of a line parallel to it is also $-\frac{3}{2}$.

Step2: Recall slope - perpendicular line relationship

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. Let the slope of the perpendicular line be $m_2$. We know $m_1 =-\frac{3}{2}$, so $-\frac{3}{2}\times m_2=-1$. Solving for $m_2$ gives $m_2=\frac{2}{3}$.

Answer:

The slope of a line parallel to the given line is $-\frac{3}{2}$. The slope of a line perpendicular to the given line is $\frac{2}{3}$.