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
