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

slope - intercept form

`y = (-2)/(3) x -(10)/(3)`

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 = (-2)/(3) x -(10)/(3)`

Final answer:-

slope - intercept form y = mx +C

`y = (-2)/(3) x -(10)/(3)`