Question

the equation of line q is y = 2/9x + 4/3. the equation of line r is y = -9/2x + 7/3. are line q and line r parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Identify the slopes

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. For line $q$ with equation $y=\frac{2}{9}x+\frac{4}{3}$, the slope $m_1=\frac{2}{9}$. For line $r$ with equation $y =-\frac{9}{2}x+\frac{7}{3}$, the slope $m_2 =-\frac{9}{2}$.

Step2: Check the relationship between slopes

Two lines are parallel if $m_1=m_2$. Here, $\frac{2}{9}
eq-\frac{9}{2}$, so they are not parallel. Two lines are perpendicular if $m_1\times m_2=- 1$. Calculate $m_1\times m_2=\frac{2}{9}\times(-\frac{9}{2})=-1$.

Answer:

perpendicular