Question

Aline passes through (-3,-2) and is perpendicular to 3x - 2y = 7.

Answer 1

Answer:

y=$-\frac{2}{3}$x-4

Step-by-step explanation:

3x-2y=7

-3x      -3x

-2y=-3x+7

/-2      /-2

y=$\frac{3}{2}$x-$\frac{7}{2}$

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 2

Answer:

y = - $\frac{2}{3}$ 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 = $\frac{3}{2}$ x - $\frac{7}{2}$ ← in slope- intercept form

with slope m = $\frac{3}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{2} }$ = - $\frac{2}{3}$, thus

y = - $\frac{2}{3}$ x + c ← is the partial equation

To find c substitute (- 3, - 2) into the partial equation

- 2 = 2 + c ⇒ c = - 2 - 2 = - 4

y = - $\frac{2}{3}$ x - 4 ← equation of perpendicular line