find the slope of a line perpendicular to the line whose equation is 4x - 6y = -24. fully simplify your…

Explanation:

Step1: Transform the equation to slope - intercept form

The slope - intercept form is (y = mx + b), where (m) is the slope. Starting with (4x-6y=-24), we solve for (y): (-6y=-4x - 24) (y=\frac{-4x-24}{-6}=\frac{2}{3}x + 4) So the slope of the given line (m_1=\frac{2}{3})

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). We know (m_1=\frac{2}{3}), and (m_1\times m_2=-1) (\frac{2}{3}\times m_2=-1) (m_2=-\frac{3}{2})

Answer:

(-\frac{3}{2})