Start with the slope-point form: #y-color(blue)(b)=color(green)(m)(x-color(red)(a))#
for a line with slope #color(green)(m)# and a point #(color(red)(a),color(blue)(b))#
Given #color(green)(m)=color(green)(-1/3#
and point #(color(red)(2),color(blue)(-7))#
We have
#color(white)("XXX")y+color(blue)(7)=color(green)(-1/3)(x-color(red)(2))#
The slope-intercept form is
#color(white)("XXX")y=color(green)(m)x+color(purple)(k)#
with the y-intercept at #color(purple)(k)#
Converting #y+color(blue)(7)=color(green)(-1/3)(x-color(red)(2))#
into slope-intercept form:
#color(white)("XXX")y=color(green)(-1/3)(x-color(red)(2))-color(blue)(7)#
#color(white)("XXX")y=color(green)(-1/3)x +2/3 -(7*3)/3#
#color(white)("XXX")y=color(green)(-1/3)x+(color(purple)(-19/3))#
Here is what it looks like as a graph:
graph{-1/3x-19/3 [-5.277, 3.492, -8.528, -4.144]}
