To find this equation we can use the point-slope formula:
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 information we are given in the problem produces:
#(y - color(red)(1)) = color(blue)(2/3)(x - color(red)(-2))#
#(y - color(red)(1)) = color(blue)(2/3)(x + color(red)(2))#
To put this into slope-intercept form (#y = mx + b#) we can solve for #y# as follows:
#(y - color(red)(1)) = color(blue)(2/3)x + (color(blue)(2/3) xx color(red)(2))#
#y - color(red)(1) = color(blue)(2/3)x + 4/3#
#y - color(red)(1) + color(green)(1) = color(blue)(2/3)x + 4/3 + color(green)(1)#
#y - 0 = color(blue)(2/3)x + 4/3 + (color(green)(1) xx 3/3)#
#y = color(blue)(2/3)x + 4/3 + color(green)(3/3)#
#y = color(blue)(2/3)x + 7/3#
