Question

Write the equation of the line through (−2, −1) and perpendicular to 2y=3x−5.

Answer 1

Y=-1

Move all terms containing x to the left side of the equation.

Subtract 3x from both sides of the equation.
2x-3x=−5


Subtract 3x from 2x


−x=-5


Multiply each term in -x=−5 by −1


Multiply each term in −x=−5 by −1

(-x) ⋅ -1=(-5) ⋅-1

X=(-5) ⋅-1

multiple -5 by -1

X=5


Since x=5 is a vertical line, the slope is undefined.
Undefined

The equation of a perpendicular line to
x=5 must have a slope that is the negative reciprocal of the original slope.

M perpendicular = -1/∞
The negative reciprocal of ∞ is 0

M perpendicular is 0



Since the slope for the perpendicular line is 0 ,the line is perpendicular to the y-axis. The equation of this line is of the form
y=c when c is any real number. The equation of the line at point (-2 ,1)

Y=-1


I hope you understand this

Answer 2

Answer:

Equation: y=-2/3x-$2\frac{2}{3}$

Step-by-step explanation:

y=mx +b

2y=3x-5

y=1.5x-2.5

y=-2/3x+b

(m is the negative reciprocal)

-2= 2/3+b

b=-2$\frac{2}{3}$

Equation: y=-2/3x-$2\frac{2}{3}$