Question

What is the equation of the line that passes through the point (-2,-2) and is perpendicular to y= -1/3x + 9?

Answer 1

`y=3x+4`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`y=-1/3x+9" is in this form"`

`"with slope "=m=-1/3`

`"Given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

`m_(color(red)"perpendicular")=-1/m`

`rArrm_(color(red)"perpendicular")=-1/(-1/3)=3`

`rArry=3x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-2,-2)" into the partial fraction"`

`-2=-6+brArrb=-2+6=4`

`rArry=3x+4larrcolor(red)"equation of perpendicular line"`