Question

write the equation of the line is perpendicular to the line y=-1/5x+9 and passes through the point -2 ,-2

Answer 1

`y=5x + 8`

Explanation:

Given line is
`y=((-1)/(5))x + 9`

so, the slope of the given line is
`(-1)/(5)`.

now, let the line which is perpendicular to the given line be y = mx + c

where,

m = slope of the line

c = constant

As we know, if two lines are perpendicular to each other, the value of product of there slopes are -1.

so, slope of given line × slope of perpendicular line = -1

⇒
`((-1)/(5))m=(-1)`

⇒
`m=5`

By substitutiong the value of m in the equation, we get;

⇒
`y=5x + c`

For c,

as the point (-2,-2) passes through the line, we get;

⇒
`-2=5(-2) + c`

⇒
`c=8`

Hence,

The line which is perpendicular to the given line and passes through (-2,-2) is

`y=5x + 8`