Question 98151
Write an equation of the line that passes through (9, 6) and is perpendicular to the line whose equation is y =-(1/3)x + 7.
:
The relationship for the slopes of perpendicular lines is: m1*m2 = -1
m1 = -1/3, find m2
(-1/3)*m2 = -1
multiply by -1
 m2 = +3; it looks like you got that part OK
:
Use the point slope equation: y - y1 = m(x - x1)
:
In this equation: m = +3; x1 = 9; y1 = 6
:
y - 6 = 3(x - 9)
y - 6 = 3x - 27
y = 3x - 27 + 6
y = 3x - 21  is perpendicular to y = -(1/3)x + 7
:
Check by substituting 9 for x in the above equation
y = 3(9) - 21
Y = 27 - 21
Y = 6
:
Should look like this:
{{{ graph( 200, 200, -25, 25, -25, 25, (-1/3)x + 7, 3x - 21) }}}