Question 162486
write the equation of a line in the form Ax+By=C through the point (-5,-3)and perpendicular to the line y= -(2/3)x+6
:
Determine the slope m2, the relationship of perpendicular lines: m1*m2=-1
Let m1 = {{{-2/3}}}
{{{-2/3}}}*m2 = -1
m2 = -1*{{{-3/2}}}
m2 = {{{3/2}}}
:
Use the point/slope formula
y - (-3) = {{{3/2}}}(x - (-5)
y + 3 = {{{3/2}}}(x +5)
y + 3 = {{{3/2}}}x + {{{15/2}}}
y  = {{{3/2}}}x + {{{15/2}}} - 3
y  = {{{3/2}}}x + {{{15/2}}} - {{{6/2}}}
y  = {{{3/2}}}x + {{{9/2}}}
Get rid of the denominators multiply equation by 2
2y = 3x + 9
arrange in the required format
-3x + 2y = 9