Respuesta :
Answer:
y=[tex]-\frac{2}{3}[/tex]x-4
Step-by-step explanation:
3x-2y=7
-3x -3x
-2y=-3x+7
/-2 /-2
y=[tex]\frac{3}{2}[/tex]x-[tex]\frac{7}{2}[/tex]
perpendicular lines always have opposite reciprocal slopes
3/2--> -2/3
y=-2/3x+b
-2=-2/3(-3)+b
-2=2+b
-2 -2
b=-4
y=-2/3x-4
Answer:
y = - [tex]\frac{2}{3}[/tex] x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3x - 2y = 7 into this form by subtracting 3x from both sides
- 2y = - 3x + 7 ( divide all terms by - 2 )
y = [tex]\frac{3}{2}[/tex] x - [tex]\frac{7}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{3}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{2} }[/tex] = - [tex]\frac{2}{3}[/tex], thus
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 3, - 2) into the partial equation
- 2 = 2 + c ⇒ c = - 2 - 2 = - 4
y = - [tex]\frac{2}{3}[/tex] x - 4 ← equation of perpendicular line
