Question

Write an equation that is perpendicular to y=5x−4 and goes through the point (10, -1)

Answer 1

Equation of the perpendicular line is
`y=-(1)/(5)x+1`

Explanation:

Given equation is y = 5x - 4

By comparing this equation with slope-intercept form of the equation,

y = mx + b

Slope of this line
`m_(1)=5`

Let the slope of the perpendicular line =
`m_(2)`

By the property of perpendicular lines,

`m_(1)* m_(2)=(-1)`

`5* m_(2)=(-1)`

`m_(2)=-(1)/(5)`

Equation of the perpendicular line passing through a point
`(x_(1), y_(1))` and slope m is represented by

`y-y_(1)=m(x-x_(1))`

If the given point is (10, -1) and slope 'm'=
`-(1)/(5)`

`y+1=-(1)/(5)(x-10)`

`y=-(1)/(5)x+2-1`

`y=-(1)/(5)x+1`