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an equation of a line that passes through the point (15,2) and is perpendicular to the line -10x+8y = 3?

Sagot :

unicorn3125

Answer:

        y = -⁴/₅x + 14

Step-by-step explanation:

Changing to slope-intercept form:

-10x + 8y = 3         {add 10x to both sides}

8y = 10x + 3         {divide both sides by 8}

y = ⁵/₄x + ³/₈

Two lines are perpendicular if the product of their slopes is equal -1:

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

y = ⁵/₄x + ³/₈   ⇒   m₁=⁵/₄

⁵/₄×m₂ = -1        ⇒    m₂ = -⁴/₅

 

The line y=-⁴/₅x+b passes through point (15, 2) so the equation:

2 = -⁴/₅×15 + b must be true

2 = -12 + b

b = 14

Therefore equation in  slope-intercept form:

                                                     y = -⁴/₅x + 14

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