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dangina [55]
3 years ago
14

Write an equation of the line with the given characteristics (show all work)

Mathematics
1 answer:
Sedbober [7]3 years ago
4 0

Answer:

1. y = - 4 x + 5

2.  x = -8

Step-by-step explanation:

1.  (-1,9) (1,1)

y = mx + b

m = (y-y') / (x-x') = (1-9) / (1-(-1)) = -8 / 2 = - 4

b = y - mx = 9 - (-4) x (-1) = 5

equation: y = - 4 x + 5

check: (1,1)   y=1 = (-4) x 1 + 5 = 1

2. Vertical line through (-8,6) is a line perpendicular to x axis

    x = -8

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Given three points A(-7, 1), B(m, 6) and P(-1, n). If the point P divides AB internally in the ratio of 3: 2, find the values of
vesna_86 [32]

Answer:

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Step-by-step explanation:

<u>Using Section Formula.</u>

<u />If \ the \ line \ segment \ AB \ where  \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \  the \ points \  of \  P  \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}<u />

   Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b  = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x =  -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3<u />

  y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4

<u />

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3 years ago
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