Question

Write an equation in Point slope intercept form that is parallel to 2x+3y=4 and passes through the point (1,-4)

Answer 1

Answer:

slope - intercept form  

 $y = \frac{-2}{3} x -\frac{10}{3}$

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

           $y = \frac{-2}{3} x -\frac{10}{3}$

Final answer:-

slope - intercept form   y = mx +C

                                    $y = \frac{-2}{3} x -\frac{10}{3}$