Question

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

Explanation:

Step1: Convert to slope-intercept form

To find the slope of the given line \(4x - 6y=-24\), we convert it to the slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
First, we isolate \(y\):

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The slope of the given line \(m_1=\frac{2}{3}\).

Step2: Find the slope of the perpendicular line

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 that \(m_1 = \frac{2}{3}\), so:

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Answer:

\(-\frac{3}{2}\)