Practice : 1. Find a line that is parallel to f(x) = 2x +3 and passes through (0,-4).

2. Find through line that is perpendicular to f(x) = 2x+3 and passes through (0,-4)

1)The equation of the Parallel line is 2x -y -4=0

2) The equation of the perpendicular line of the given line x+2y+8=0

Step-by-step explanation:

Step(i):-

Given function f(x) = 2x+3 and passes through (0,-4)

Let y =f(x) = 2x+3

    y = 2x+3

⇒ 2x -y +3=0

The equation of the parallel line of the given line 2x - y +k =0

This line is passes through the point (0,-4)

⇒ 2 (0) -(-4)+k=0

            4 +k=0

        ⇒    k =-4

The equation of the Parallel line is 2x -y -4=0

2)

Step(ii):-

Given function f(x) = 2x+3

Let y = 2 x + 3

 2x - y +3=0

The equation of the perpendicular line   bx -ay +k=0

The equation of the perpendicular line of the given line -x-2y +k =0

This line is passes through the point (0,-4)

⇒  (0) -2(-4)+k=0

            8 +k=0

        ⇒    k =-8

The equation of the perpendicular line of the given line -x-2y -8 =0

The equation of the perpendicular line of the given line x+2y+8=0

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4