Question

What is the equation of the line perpendicular to `y=1/4x` that passes through `(-7,4)`?

Answer 1

`y=-4x-24`

Explanation:

`y=1/4x" is in "color(blue)"slope-intercept form"` that is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept.

`rArry=1/4x" has slope " =m=1/4`

The slope of a line perpendicular to this is `color(blue)"the negative reciprocal"` of m

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

The equation of a line in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where `(x_1,y_1)" is a point on the line"`

`"using " m=-4" and " (x_1,y_1)=(-7,4)`

`y-4=-4(x-(-7))`

`rArry-4=-4(x+7)larrcolor(red)" in point-slope form"`

`"distributing and simplifying gives"`

`y-4=-4x-28`

`rArry=-4x-24larrcolor(red)" in slope-intercept form"`