Question

What slope would make the lines perpendicular? y = 4x + 2 y = -x + 2 Enter the number that belongs in the green box.​

Answer 1

The missing number in the green box is 4

Explanation:

The product of the slopes of the perpendicular lines is -1, which means

• if the slope of one of them is m, then the slope of the perpendicular line to it is the negative reciprocal (
  `(-1)/(m)`)

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept

Let us solve the question

∵ The equation of the first line is y = 4x + 2

→ Compare it with the form of the linear equation above

∴ m = 4

∵ m is the slope

∴ The slope of the line is 4

∵ The slope of the perpendicular line should be the negative reciprocal of it

∵ The negative reciprocal of 4 is
`-(1)/(4)`

∴ The slope of the perpendicular line is
`-(1)/(4)`

→ Substitute it in the equation

∴ y =
`-(1)/(4)` x + 2

∴ The missing number in the green box is 4