MATH SOLVE

3 months ago

Q:
# Find the value of n so that the line perpendicular to the line with the equation -2y + 4 = 6x + 8 passes through the points at (n, -4) and (2, -8).

Accepted Solution

A:

If the line must be perpendicular to the equation, that means the slope is the reciprocal of the one in the given equation. So first we find that, the slope of the given equation.

- 2y + 4 = 6x + 8

- 2y = 6x + 4

y = - 3x - 2

So the slope of the given equation is - 3x. That means the slope of our perpendicular equation must be 1/3x

Now to find the value of n, plug in our given information and perpendicular slope into the slope equation:

Slope = (Y₂ - Y₁ ) / (X₂ - X₁)

1/3 = (- 8 - (-4)) / (2 - n)

1/3 = (- 8 + 4) / (2 - n)

1/3 = ( - 4) / (2 - n)

Multiply both sides by (2 - n) to get the binomial out of the denominator

(1/3)(2 - n) = - 4

Multiply both sides by 3 to isolate the binomial

2 - n = - 4(3)

2 - n = - 12

Subtract 2 from both sides to isolate the variable

- n = - 14

Divide by - 1 to get rid of the negative.

n = 14. Your coordinate is ( 14, - 4)

Now to find the equation that is perpendicular.

y = 1/3x + b

Plug in either of the coordinates. I'm going to use the ordered pair we just found.

- 4 = 1/3(14) + b

- 4 = 14/3 + b

- 12/3 = 14/3 + b

Subtract 14/3 on both sides.

- 26/3 = b

Your equation is y = 1/3x - 26/3

- 2y + 4 = 6x + 8

- 2y = 6x + 4

y = - 3x - 2

So the slope of the given equation is - 3x. That means the slope of our perpendicular equation must be 1/3x

Now to find the value of n, plug in our given information and perpendicular slope into the slope equation:

Slope = (Y₂ - Y₁ ) / (X₂ - X₁)

1/3 = (- 8 - (-4)) / (2 - n)

1/3 = (- 8 + 4) / (2 - n)

1/3 = ( - 4) / (2 - n)

Multiply both sides by (2 - n) to get the binomial out of the denominator

(1/3)(2 - n) = - 4

Multiply both sides by 3 to isolate the binomial

2 - n = - 4(3)

2 - n = - 12

Subtract 2 from both sides to isolate the variable

- n = - 14

Divide by - 1 to get rid of the negative.

n = 14. Your coordinate is ( 14, - 4)

Now to find the equation that is perpendicular.

y = 1/3x + b

Plug in either of the coordinates. I'm going to use the ordered pair we just found.

- 4 = 1/3(14) + b

- 4 = 14/3 + b

- 12/3 = 14/3 + b

Subtract 14/3 on both sides.

- 26/3 = b

Your equation is y = 1/3x - 26/3