Write an equation for the line that is parallel to the given line and that passes through the given point.
-x + 5y = 14; (-5,-2)

a.) y = -1/5x - 27

b.) y = 5x - 27

c.) y = -1/5x -15

d.) y = -5x -27

Answers

To determine the equation that would be perpendicular with a certain line, we must first know the characteristics of a perpendicular line. This line would have a 90 degrees angle with another line so that the slope of this line would be the negative reciprocal of the slope of the other line. To write the equation, given a certain point we use the point-slope form of a line, y -y1 = m(x - x1).

Original line: -x + 5y= 14
                              y = x/5 + 14/5
                       slope = 1/5

Perpendicular line's slope = -5
                         y - y1 = m (x - x1)
                         y - (-2) = -5 (x - (-5))
                                  y = -5x - 25 -2
                                  y = -5x -27
The answer is y=5x-27
Solve them all? Or are these options
Idk what it is but ik what can ( not tryna be rude ) download these apps : photo math, quizlet ( if the problem stars with a upper case letter it’s made by the teacher if it’s all lower case it’s on quizlet ).

y -y1= m(x-x1)  is in point slope form

y --9 = -2 (x-10)

y+9 = -2(x-10)

Step-by-step explanation:

•x + y < 6

(6,6)

• 5x + y = 10

(2,10)

•x + 5y = 14

(14,14/5)

intersection I

x + 5y = 14

5x + y = 10

____________ •2

5x + 25y = 70

5x + y = 10

____________ _

24y = 60

y = 2 1/2 = 2,5

substitusion

5x + y = 10

5x + 2,5 = 10

5x = 7,5

x = 1,5

(1,5 , 2,5)

Intersection II

x + y = 6

5x + y = 10

_____________ _

-4x = -4

x = 1

x + y = 6

y = 6 - 1

y = 5

(1 , 5)

Intersection III

x + y = 6

x + 5y = 14

___________ _

-4y = -8

y = 2

x + y = 6

x = 6 - 2

x = 4

(4 , 2)

SUBSTITUSION

p = 10x + 26y

I.(1,5 , 2,5) = 10(1,5) + 26(2,5) = 15 + 65 = 80. (MINIMUM)

II.(1,5) = 10(1) + 26(5) = 10 + 130 = 140(MAXIMUM)

III.(4,2) = 10(4) + 26(2) = 40 + 52 = 92

SO,MINIMUM VALUE ------> 80


Min p = 10x + 26y subject to x+y< 6 5x+y> 10 x+5y> 14

Option a

y + 9 = –2(x – 10)

Step-by-step explanation:

Given that a line passes through (10,-9) and slope =-2

We know that a point slope formula is

y-y_1 =m(x-x_1)\\

Here x_1 =10:  y_1=-9:\\m=-2

Substitute this in the eqution to get

y-(-9) =-2(x-10)\\

Simplifying this

y+9=-2(x-10)

Option a) is right.

a)

x + 3y = 14|\cdot(-3)\\3x + y = 10\\\\-3x - 9y = -42\\3x + y = 10\\\\-8y = -32 = y = 4, x = 14 - 12 = 2\\(2, 4)

b)

5x + y = 27|\cdot(-3)\\4x + 3y = 26\\\\-15x - 3y = -81\\4x + 3y = 26\\\\-11x = - 55 = x=5, y = 27-25 = 2\\(5, 2)

c)

-6x + 5y = -14\\-2x + y = -6| \cdot(-3)\\\\-6x + 5y = -14\\6x - 3y = 18\\\\2y = 4 = y = 2, x = -1/2\cdot(-6 -2) = 4\\(4, 2)

d)

2x + 5y = 14\\3x + y = -5|\cdot(-5)\\\\2x + 5y = 14\\-15x - 5y = 25\\\\-13x = 39 = x = -3, y = 1/5\cdot(14 - 2(-3)) = 4\\(-3, 4)

e)

-3x + 2y = 6\\x + 4y = -9|\cdot3\\\\-3x + 2y = 6\\3x + 12y = -27\\\\14y = -21 = y = -\frac{3}{2}, x = -3\\(-3, -1.5)

f)

3x - 5y = 7\\x + y = -11|\cdot(5)\\\\3x - 5y = 7\\5x + 5y = -55\\\\8x = -48= x= -6, y = -11 + 6 = -5\\(-6, -5)

g)

2x + 3y = 9|\cdot(-2)\\4x + y = -7\\\\-4x - 6y = -18\\4x + y = -7\\\\-5y = -25 = y = 5, x = 1/4(-7-5) = -3\\(-3, 5)

h)

-x + 5y = 7|\cdot(-1)\\5x + 5y = 19\\\\x-5y = -7\\5x + 5y = 19\\\\6x = 12 = x = 2, y = (7 + 2)/5 = \frac{9}{5}\\(2, 1.8)

y=5x-27

Step-by-step explanation:

The answer would be D



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