Question

find the slope of a line perpendicular to the line whose equation is 3x + 2y = 14. fully simplify your answer.

Explanation:

Step1: Convert to slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
We start with the given equation $3x+2y = 14$.
Subtract $3x$ from both sides: $2y=-3x + 14$.
Divide each term by 2: $y=-\frac{3}{2}x + 7$.
So the slope of the given line, $m_1=-\frac{3}{2}$.

Step2: Find the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of the perpendicular line be $m_2$.
We know that $m_1\times m_2=-1$.
Substitute $m_1 = -\frac{3}{2}$ into the equation: $-\frac{3}{2}\times m_2=-1$.
Solve for $m_2$ by multiplying both sides by $-\frac{2}{3}$: $m_2=(-1)\times(-\frac{2}{3})=\frac{2}{3}$.

Answer:

$\frac{2}{3}$