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2 years ago

3. Write an equation of the line that passes through (-2, 8) and (4,4).

Mathematics

1 answer:

gtnhenbr [62]2 years ago

4 0

$y = - \frac{2}{3} x + \frac{20}{3}$

Step-by-step explanation:

y=mx+c

label your points

(-2;8). pnt2

(4;4). pnt1

$m = \frac{y2 - y1}{x2 - x1}$

$m = \frac{8 - 4}{ - 2 - 4}$

$m = \frac{ 4}{ - 6}$

$m = - \frac{2}{3}$

substitute gradient and 1 point into equation to get c

$8 = ( - \frac{2}{3} )( - 2) + c$

$8 = \frac{4}{3} + c$

$c = 8 - \frac{4}{3}$

$c = \frac{20}{3}$

Therefore the equation is

$y = - \frac{2}{3} x + \frac{20}{3}$

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STEP 1: See attached drawing on graph paper

STEP 2:

Length of segment 1 - 2 = 100 feet

Length of segment 2 - 3 = 89.44 ft.

Length of segment 3 - 4 = 186.82 ft.

Length of segment 4 - 5 = 120.83 ft.

Length of segment 5 - 1 = 136.01 ft.

STEP 3:

The perimeter of the property is 633.103 ft.

STEP 4:

The cost of fencing by Company 1 is $7597.24

The cost of fencing by Company 2 is $8246.55

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Step-by-step explanation:

STEP 1: See attached drawing on graph paper

STEP 2:

Therefore, we have

Length of segment 1 - 2 = √(8² + 6²) = 10 × 10 = 100 feet

Length of segment 2 - 3 = √(4² + 8²) = 4·√5× 10 = 40·√5 feet = 89.44 ft.

Length of segment 3 - 4 = √(5² + 18²) = √349 = 10·√349 feet = 186.82 ft.

Length of segment 4 - 5 = √(11² + 5²) = √146 = 10·√146 feet = 120.83 ft.

Length of segment 5 - 1 = √(11² + 8²) = √185 = 10·√185 feet = 136.01 ft.

STEP 3:

Therefore, the perimeter of the property = 100 + 89.44 + 186.82 + 120.83 + 136.01 = 633.103 ft.

STEP 4:

Hence the cost of fencing the property by Company 1 = $12 × 633.103 = $7597.24

The cost of fencing the property by Company 2 = $250 + $15 × 533.103 = $8246.55.

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