Question

How do you find the general form of the line that passes through A(3, -4); perpendicular to the line 2x - 6y = 11?

Answer 1

`3x+y-5=0`

Explanation:

`"the equation of a line in "color(blue)"general form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By+C=0)color(white)(2/2)|)))`

`"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-6y=11" into this form"`

`rArr6y=2x-11`

`rArry=1/3x-11/6larrcolor(red)"in slope-intercept form"`

`rArr"slope "=m=1/3`

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

`rArry=-3x+b color(blue)" is the partial equation"`

`"to find b substitute "(3,-4)" into the partial equation"`

`-4=-9+brArrb=5`

`rArry=-3x+5larrcolor(red)"in slope-intercept form"`

`rArr3x+y-5=0larrcolor(red)"in general form"`