A line going through the points #(0,7)# and #(3,5)# has a slope of
#color(white)("XXX")color(green)m=(Deltay)/(Deltax)=(7-5)/(0-3)=color(grenn)(-2/3)#
The general slope-point form for a linear equation is
#color(white)("XXX")y-color(blue)(y_1)=color(green)m(x-color(red)(x_1))#
for a line through the point #(color(red)(x_1),color(blue)(y_1))# and with a slope of #color(green)(m)#
We have already determined #color(green)m=color(green)(-2/3)#
and we can arbitrarily select either of the given points for #(color(red)(x_1),color(blue)(y_1))#
For demonstration purposes, I will use #(color(red)(x_1),color(blue)(y_1))=(color(red)0,color(blue)7)#
So our slope-point form becomes
#color(white)("XXX")y-color(blue)7=color(green)(-2/3)(x-color(red)0)#
While this is a perfectly valid answer, it is common to convert this into "standard form": #Ax+By=C#, with #A,B,C in ZZ, A>=0#
#color(white)("XXX")y-7=-2/3(x-0)#
#color(white)("XXX")rarr 3y-21=-2x#
#color(white)("XXX")rarr 2x+3y=21#
