Question

What is the equation of the line in slope-intercept form that passes through the point (3, –5) and is perpendicular to y = –3x – 4?

Answer 1

`y=1/3x-6`

Explanation:

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

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

`y=-3x-4" is in "color(blue)"slope-intercept form"`

`•color(white)(x)y=mx+b`

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

`rArry=-3x-4" has slope "m=-3`

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

`rArry=1/3x+blarr" partial equation"`

`"to find b substitute "(3,-5)" into the partial equation"`

`-5=1+brArrb=-6`

`rArry=1/3x-6larrcolor(red)" in slope-intercept form"`