Question 333064
write the equation of the line in slope intercept form through the point coordinates (-4,6) and perpendicular to 3x-2y=8.
:
Find the slope by putting the equation into the slope/intercept form (y=mx+b)
3x - 2y = 8
-2y = -3x + 8
y has to be positive, multiply by -1
2y = 3x - 8
divide both sides by 2
y =  {{{3/2)))x - {{{8/2}}}
y = {{{3/2}}}x - 4
Slope: m1 = {{{3/2}}}
;
slope relationship of the slopes of perpendicular lines is m1*m2 = -1
find m2
{{{3/2}}}*m2 = -1
m2 = -1 * {{{2/3}}}
m2 = {{{-2/3}}} is the slope of the perpendicular line
:
Find the equation using the point/slope form: y - y1 = m(x - x1)
m = {{{-2/3}}}, x1 = -4, y1 = 6
y - 6 = {{{-2/3}}}(x - (-4))
y - 6 = {{{-2/3}}}(x + 4)
y - 6 = {{{-2/3}}}x + (-2/3)*4
y - 6 = {{{-2/3}}}x - {{{8/3}}}
y = {{{-2/3}}}x - {{{8/3}}} + 6
y = {{{-2/3}}}x - {{{8/3}}} + {{{18/3}}}
y = {{{-2/3}}}x + {{{10/3}}} is the equation of the perpendicular line
:
:
Check by finding y when x = -4
y = {{{-2/3}}}(-4) + {{{10/3}}}
y = {{{8/3}}} + {{{10/3}}}
y = {{{18/3}}}
y = 6