find the slope of a line perpendicular to the line whose equation is 4x - 3y = -3. fully simplify your answer.

Explanation:

Step1: Rewrite the given equation in slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the slope. Starting with $4x−3y=-3$, we solve for $y$: $-3y=-4x - 3$, then $y=\frac{4}{3}x + 1$. So the slope of the given line $m_1=\frac{4}{3}$.

Step2: Use the perpendicular slope formula

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. Let the slope of the perpendicular line be $m_2$. We know $m_1=\frac{4}{3}$, then $\frac{4}{3}\times m_2=-1$. Solving for $m_2$, we get $m_2=-\frac{3}{4}$.

Answer:

$-\frac{3}{4}$