Question

How do you write an equation through point (-1,-8), perpendicular to y= -3/4x + 4?

Answer 1

`y=4/3x-20/3`

Explanation:

`y=-3/4x+4" is in the form "color(red) (y=mx+b)` where m represents the slope and b the y-intercept.

`rArrm=-3/4`

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

`rArrm_("perpendicular")=-1/(-3/4)=4/3`

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"`

`"here "m=4/3" and " (x_1,y_1)=(-1,-8)`

`rArry-(-8)=4/3(x-(-1))`

`rArry+8=4/3(x+1)larrcolor(red)"in point-slope form"`

Distributing the bracket and simplifying gives an alternative version of the equation.

`y+8=4/3x+4/3`

`rArry=4/3x+4/3-8`

`rArry=4/3x-20/3larrcolor(red)" in slope-intercept form"`