Answer:
slope - intercept form
[tex]y = \frac{-2}{3} x -\frac{10}{3}[/tex]
Step-by-step explanation:
Step(i)
Given that the equation of the line 2 x+3 y = 4
The equation of the parallel line to the given straight line is
a x +b y + k=0
The equation of the Parallel line to the given straight line is
2x+3y+k=0
This line is passes through the point (1,-4)
2(1) +3(-4)+k=0
⇒ 2-12 +k=0
⇒ -10 +k=0
⇒ k =10
Step(ii):-
The equation of the parallel line to the given straight line is
2 x + 3y + 10 =0
3 y = -2x -10
[tex]y = \frac{-2}{3} x -\frac{10}{3}[/tex]
Final answer:-
slope - intercept form y = mx +C
[tex]y = \frac{-2}{3} x -\frac{10}{3}[/tex]
