The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the point and slope from the problem gives the equation:
#(y - color(red)(3)) = color(blue)(-2/3)(x - color(red)(9))#
We can also convert to the more familiar slope-intercept form if we solve for #y#.
The slope-intercept form of a linear equation is:
#y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b# is the y-intercept value.
#y - color(red)(3) = (color(blue)(-2/3) xx x) - (color(blue)(-2/3) xx color(red)(9))#
#y - color(red)(3) = -2/3x - (-6)#
#y - color(red)(3) = -2/3x + 6#
#y - color(red)(3) + 3 = -2/3x + 6 + 3#
#y - 0 = -2/3x + 9#
#y = -2/3x + 9#
