Question

Can you assist me with this? Express the equation in general form or slope-intercept form.

Perpendicular to the line 4x+y=-22, and contains the point (-8,9)

Answer 1

Hence, the equation of the normal is
`y=1/4x+11`

Explanation:

Given, a straight line `4x+y=22`
Expressing in standard form `ax+by+c=0`
Line is `4x+y-22=0`
Comparing we have `a=4, b=1`
Slope of the line `4x+y-22=0` is given by
`m=-a/b=-4/1=-4`

Slope of the normal to the line `4x+y=22`is given by+`m'=-1/m`
`m'=-1/-4=1/4`
The line passes through the point `(-8,9)`

Intercept given by

`c'=y_1-m'x_1=9-1/4xx(-8)=9+2=11`

The normal in the slope intercept form is
`y=m'x+c'=1/4x+11`

Hence, the equation of the normal is
`y=1/4x+11`

Answer 2

`y=1/4x+11`

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 "4x+y=-22" into this form"`

`"subtract 4x from both sides"`

`cancel(4x)cancel(-4x)+y=-4x-22`

`rArry=-4x-22larrcolor(red)"in slope-intercept form"`

`rArrm=-4`

`"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/(-4)=1/4`

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

`"to find b substitute "(-8,9)" into the partial equation"`

`9=-2+brArrb=9+2=11`

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

`"or "x-4y+44=0larrcolor(red)"in general form"`