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What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5 ? Enter your answer in the box.

User Spectrum
by
9.4k points

2 Answers

1 vote

Answer:

Answer: the equation is y'=
(3)/(2)x'-11

Explanation:

A line is given whose equation is given as
y=-(2x)/(3)+5------(1)

and we have to find the equation of another line which is perpendicular to this.

Let the equation of the line be y'=mx'+c------(2)

This line passes through a point (8,1) so we put the values of x & y in the equation.

⇒ 1 = m×8+c

⇒ 8m+c = 1------(3)

We know that if two lines are perpendicular to each other then multiplication of their slopes is equal to (-1).

Therefore m×
(-(2)/(3))=(-1)


(2)/(3) m=1

⇒m=
(3)/(2)

Now we put the value of m in equation (3) to get the value of c


((3)/(2))+c = 1

12+c=1

c = (-11)

Therefore the equation will be y'=
(3)/(2)x'+(-11)

User Cia
by
8.0k points
2 votes

Answer:


y = (3)/(2) x-11

Step-by-step explanation:

We are to find the equation a line that passes through the point (8, 1) and which is perpendicular to a line whose equation is
y = - (2)/(3) x+5.

We know that the slope of line which is perpendicular to another line is the negative reciprocal of the slope of the other line so it will be
(3)/(2).

Then, we will find the y-intercept of the line using the standard equation of a line:


y=mx+c


1=(3)/(2) (8)+c


c=-11

Therefore, the equation of the line will be
y = (3)/(2) x-11.


User Jmertic
by
8.2k points

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