Question

How do you write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6)?

Answer 1

`y=1/4x+11/2`

Explanation:

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

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

`"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=-4x" is in this form"`

`"with slope "m=-4`

`rArrm_(color(red)"perpendicular")=-1/(-4)=1/4`

`rArry=1/4x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(2,6)" into the partial equation"`

`6=1/2+brArrb=12/2-1/2=11/2`

`rArry=1/4x+11/2larrcolor(red)"in slope-intercept form"`