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

1 Answer
Mar 16, 2017

Answer:

#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"#