Question

Write down the equation of a line perpendicular to y = 1/2x - 4 which passes through (0,7)

(i got the answer y = 2x + 7, can anyone confirm if this is right/wrong?)

Answer 1

Perpendicular Lines

Perpendicular lines have slopes that are negative reciprocals of each other.

Solving the Question

We're given:

• Perpendicular to
  `y =(1)/(2)x - 4`
• Passes through (0,7)

First, we must find the slope.

• The negative reciprocal of
  `(1)/(2)` is -2.
• Plug this into
  `y=mx+b`:

• 
  `y=-2x+b`

The y-intercept occurs when x=0. Therefore, given the point (0,7), we know that the y-intercept is 7:

• 
  `y=-2x+7`

Answer

`y=-2x+7`

Answer 2

y = -2x + 7

Explanation:

The slopes of perpendicular lines are negative reciprocals.

That means that their product is -1.

If the slope of a line is m, then a perpendicular line has slope -1/m.

Given line slope: 1/2

Perpendicular slope: -2

Perpendicular line:

y = -2x + b

Point on new line: (0, 7)

7 = -2(0) + b

b = 7

Perpendicular line:

y = -2x + 7