Question 376082
write an equation in standard form of the line that contains the
 point (-1, 2) and is perpendicular to the line y=3x-1
:
slope of the equation, m1 = 3
:
The relationship of slopes of perpendicular lines: m1*m2 = -1
3*m2 = -1
m2 = {{{-1/3}}} is the slope of the perpendicular line
:
Use point slope form to find the equation of the line, y - y1 = m(x - x1)
where m2={{{-1/3}}}, x1=-1, y1=2
:
y - 2 = {{{-1/3}}}(x - (-1))
y - 2 = {{{-1/3}}}(x + 1)
y - 2 = {{{-1/3}}}x - {{{1/3}}}
y = {{{-1/3}}}x - {{{1/3}}} + 2
y = {{{-1/3}}}x - {{{1/3}}} + {{{6/3}}}
y = {{{-1/3}}}x + {{{5/3}}}; is the equation of the perpendicular line
But they want it in the standard form
Multiply equation by 3, to get rid of the denominators
3y = -x + 5
x + 3y = 5; is the standard form
:
looks like this
{{{ graph( 300, 300, -5, 5, -4, 4, 3x-1, (-1/3)x+(5/3)) }}}