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 values from the point and the slope given in the problems allows us to write this equation:
#(y - color(red)(-2)) = color(blue)(1/3)(x - color(red)(3))#
#(y + color(red)(2)) = color(blue)(1/3)(x - color(red)(3))#
We can also transform this to the slope-intercept form by solving 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)(2) = (color(blue)(1/3) xx x) - (color(blue)(1/3) xx color(red)(3))#
#y + color(red)(2) = 1/3x - 1#
#y + color(red)(2) - 2 = 1/3x - 1 - 2#
#y + 0 = 1/3x - 3#
#y = color(red)(1/3)x - color(blue)(3)#
