Question

How do you write the equation in slope intercept form perpendicular to the line 2x -3y = 12 and passes through the point (2, 6)?

Answer 1

`y=-3/2x+9`

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"`

`"rearrange "2x-3y=12" into this form"`

`"subtract 2x from both sides"`

`rArr-3y=-2x+12`

`"divide all terms by "-3`

`rArry=2/3x-4larrcolor(blue)"in standard form"`

`"with "m=2/3`

`"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`

`rArrm_("perpendicular")=-1/(2/3)=-3/2`

`rArry=-3/2x+blarrcolor(blue)"is the partial equation"`

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

`6=-3+brArrb=6+3=9`

`rArry=-3/2x+9larrcolor(red)"equation of perpendicular line"`