Question

What is the equation of the line perpendicular to `y=2/7x` that passes through `(-2,9)`?

Answer 1

`y=-7/2x+2`

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=2/7x" is in this form"`

`"with slope m "=2/7" and "b=0`

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

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

`rArrm_("perpendicular")=-1/(2/7)=-7/2`

`rArry=-7/2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-2,9)" into the partial equation"`

`9=7+brArrb=9-7=2`

`rArry=-7/2x+2larrcolor(red)"perpendicular equation"`

Answer 2

See details below

Explanation:

The general equation of a stright line is `y=mx+n`

where m is the slope and n is y-intercept

We know also that if m is the slope, then `-1/m` is the slope of perpendicular line to the line given. In our case, we have

`m=2/7`, and `n=0` then the slope of perpendicular is `m'=-7/2`

The reuqested equation is `y=-7/2x+n`

We dont know what is the n value, but they asking for a line perpendicular passing thru `(-2,9)`, Then this point acomplish the line equation. That means `9=-7/2·(-2)+n`

Transposing terms we found `n=2`. Finally the equation is

`y=-7/2x+2`
See graph below (A is the given point)