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

What Slope Would Make The Lines Perpendicular Y 4x 2 Y X 2 Enter The Number That Belongs In The Green Box class=

Sagot :

Ashraf82idn

Answer:

The missing number in the green box is 4

Step-by-step 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 ([tex]\frac{-1}{m}[/tex])

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 [tex]-\frac{1}{4}[/tex]

∴ The slope of the perpendicular line is [tex]-\frac{1}{4}[/tex]

→ Substitute it in the equation

∴ y = [tex]-\frac{1}{4}[/tex] x + 2

∴ The missing number in the green box is 4

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