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3 years ago

What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)

Mathematics

1 answer:

Andrews [41]3 years ago

7 0

<h2>Answer: y = ⁵/₂ x - 13 OR y + 8 = ⁵/₂ x - 5 </h2>

<h3>Step-by-step explanation:</h3>

Find the slope of the perpendicular line

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

⇒ if the slope of this line = - ²/₅

then the slope of the perpendicular line (m) = ⁵/₂

Determine the equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - (-8) = ⁵/₂ (x - 2)

∴ y + 8 = ⁵/₂ (x - 2)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

since y + 8 = ⁵/₂ (x - 2)

y = ⁵/₂ x - 13

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Fiona is trying to prove that a pair of expressions are equivalent by using substitution. Which pair of expressions has the same

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Missing Part of the Question

3 (4 - y) -7 ; 5 + 3y

9 + y + 4y - 2 - 3y; -2y + 7

5 + y - 2 - 6y + y; 8y + 3

2y + 7 + y - 2 + y; 4y + 5

Answer:

2y + 7 + y - 2 + y; 4y + 5

Step-by-step explanation:

Given

y = 3

Required

Which pair of expression are equal

To get the pair of expression that are equal; we simply substitute 3 for y in each of the expressions

3 (4 - y) -7 and 5 + 3y

Substitute 3 for y in 3 (4 - y) -7

This gives 3(4 - 3) -7

= 3(1) - 7

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This gives 5 + 3(3)

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---------------------------------------------------------------------------------------

9 + y + 4y - 2 - 3y; -2y + 7

Substitute 3 for y in 9 + y + 4y - 2 - 3y

This gives 9 + 3 + 4(3) - 2 - 3(3)

= 9 + 3 + 12 - 2 - 9

= 13

Then Substitute 3 for y in -2y + 7

This gives -2(3) + 7

= -6 + 7

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5 + y - 2 - 6y + y; 8y + 3

Substitute 3 for y in 5 + y - 2 - 6y + y

This gives 5 + 3 - 2 - 6(3) + 3

= 5 + 3 - 2 - 18 + 3

= -9

Then Substitute 3 for y in 8y + 3

This gives 8(3) + 3

= 24 + 3

= 27

-9 and 27 are not equal

---------------------------------------------------------------------------------------

2y + 7 + y - 2 + y; 4y + 5

Substitute 3 for y in 2y + 7 + y - 2 + y

This gives 2(3) + 7 + 3 - 2 + 3

= 6 + 7 + 3 - 2 + 3

= 17

Then Substitute 3 for y in 4y + 5

This gives 4(3) + 5

= 12 + 5

= 17

17 and 17 are equal

Hence, Option D is correct

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Answer:

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Step-by-step explanation:

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What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)​

What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)