what is the slope of a line that is perpendicular to the line 2y - 3x = 8?\n-3\n-\\frac{2}{3}\n\\frac{1}{3}\n…

what is the slope of a line that is perpendicular to the line 2y - 3x = 8?\n-3\n-\\frac{2}{3}\n\\frac{1}{3}\n\\frac{3}{2}

what is the slope of a line that is perpendicular to the line 2y - 3x = 8?\n-3\n-\\frac{2}{3}\n\\frac{1}{3}\n\\frac{3}{2}

Answer

Answer:

B. $-\frac{2}{3}$

Explanation:

Step1: Rewrite the given line in slope - intercept form

First, rewrite $2y - 3x=8$ as $y=\frac{3}{2}x + 4$. The slope of this line $m_1=\frac{3}{2}$.

Step2: Use the perpendicular - slope formula

If two lines are perpendicular, the product of their slopes $m_1\times m_2=- 1$. Let the slope of the perpendicular line be $m_2$. Then $\frac{3}{2}\times m_2=-1$. Solving for $m_2$, we get $m_2 =-\frac{2}{3}$.