Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−23x+5y=−23x+5 ? enter your answer in the box?

Answer 1

The correct answer is: y=3/2x-11 :D

Answer 2

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

Explanation:

We have been given an equation
`y=-(2)/(3)x+5`. We are asked to find the equation of line perpendicular to our given equation and passes through point (8,1).

We know that the slope of a perpendicular line to a given line is negative reciprocal of the slope of given line. So the slope of perpendicular line to the line
`y=-(2)/(3)x+5` will be negative reciprocal of
`-(2)/(3)`.

`\text{negative reciprocal of }-(2)/(3)=-(-(3)/(2))`

`\text{negative reciprocal of }-(2)/(3)=(3)/(2)`

Upon substituting
`m=(3)/(2)` and coordinates of point (8,1) in slope intercept form of equation we will get,

`1=(3)/(2)*8+b`

`1=3*4+b`

`1=12+b`

`1-12=12-12+b`

`-11=b`

Therefore, the equation
`y=(3)/(2)x-11` represents the equation of line perpendicular to our given line.