Question

How do you determine whether the lines for each pair of equations $3x+2y=-5$, $y=-\frac{2}{3}x+6$ are parallel, perpendicular, or neither?

Answer 1

Step 1. Find the slope of the equations:

Given, that the pair of line equations are $3x+2y=-5$and $y=-\frac{2}{3}x+6$.

The lines are parallel if slopes are equal and are perpendicular if the product equals minus one.

The equation's $y=mx+c$ slope expressed as $m$.

Hence, the slope of $y=-\frac{2}{3}x+6$is $-\frac{2}{3}$

The equation's $ax+by+c=0$ is expressed as $-\frac{a}{b}$.

Thus, the slope of the equation $3x+2y=-5$can be written as $3x+2y+5=0$ and is expressed as $-\frac{3}{2}$.

Step 2. Find the pair of equations $3x+2y=-5$, $y=-\frac{2}{3}x+6$ are parallel, perpendicular, or neither:

The provided pair of lines are not parallel if the slopes are observed to be unequal.

The slopes' product is represented as $-\frac{2}{3}\times -\frac{3}{2}=1$.

The lines are not perpendicular as a result.

Therefore, the given pair of lines are therefore neither parallel nor perpendicular.