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Elanso [62]
3 years ago
6

I don't know how to do this please help. Thank you

Mathematics
1 answer:
Andreyy893 years ago
7 0
Let y = \frac{4}{3} x be L₁  & the unknown be L₂

Now, if L₂ is perpendicular to L₁ then the product of their gradient (m) is -1.  This implies that the gradient of L₂ is the negative reciprocal of L₁:

∴ if m of  L₁ = \frac{4}{3}

then m of L₂ = - \frac{3}{4}

Now since L₂ passes through the line (4, 2),

then by using the point-slope form (y - y₁) = m (x - x₁)
     ⇒      (y - 2) =  - \frac{3}{4} (x - 4)
     ⇒   4 (y - 2) = -3 (x - 4)
     ⇒      4y - 8 = -3x + 12
     ⇒    4y + 3x = 20

∴ the line that passes through the point (4,2) that is perpendicular to the line y = 4/3x  is characterized by the equation  4y + 3x = 20
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3x-2y=17........(1)

x=4y-1

substituting value of x in equation 1

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again

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