Respuesta :
Answer:
y = [tex]\frac{2}{3}[/tex] x - 9
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 2x - 3y = 6 into this form
subtract 2x from both sides
- 3y = - 2x + 6 ( divide all terms by - 3 )
y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form
with m = [tex]\frac{2}{3}[/tex]
• Parallel lines have equal slopes, hence
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
to find c substitute (9, - 3) into the partial equation
- 3 = 6 + c ⇒ c = - 3 - 6 = - 9
y = [tex]\frac{2}{3}[/tex] x - 9 ← equation of parallel line
Answer:
-2x + 3y = -27
or
y = 2/3 x - 9
Step-by-step explanation:
First convert to slope-intercept form to find the slope of the given line.
2x - 3y = 6
-3y = -2x + 6
Divide through by -3:-
y = 2/3 x - 2
x = 9 when y = -3 so using the point slope form of an equation:-
y - (-3) = 2/3 (x - 9)
y + 3 = 2/3 x - 6
y = 2/3 x - 9
The slope is the same as the given equation so the lines are parallel.
We can now change this to standard form:-
3y = 2x - 27
-2x + 3y = -27
