Question

How do you write the equation of a line that is perpendicular to the line represented by `2x - y = 7`?

Answer 1

`y=-1/2x-7`

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-y=7" into this form"`

`"add "y" to both sides"`

`rArr2x=y+7`

`"subtract 7 from both sides"`

`rArry=2x-7larrcolor(blue)"in slope-intercept form"`

`"with slope m "=2" and y-intercept "=-7`

`"given the equation of 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`

`"the equation of a perpendicular line "`

`"with "m=-1/2" and y-intercept "=-7" is"`

`y=-1/2x-7`