Which equation represents a line which is perpendicular to the line 5x + 2y = 12?

Step-by-step explanation:

Changing to slope-intercept form:

5x + 2y = 12         {subtract 5x from both sides}

2y = -5x + 12         {divide both sides by 2}

y = -⁵/₂ x + 6

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y =-⁵/₂ x + 1    ⇒     m₁ =  -⁵/₂

-⁵/₂× m₂ = -1      ⇒   m₂ = ²/₅

So, any line perpendicular to 5x + 2y = 12 must have slope m =²/₅

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