To find the #x# and #y# intercept you substitute #0# for one of the variables and solve for the other variable.

x-intercept:

Substitute #0# for #y# and solve for #x#

#3 = 7x + (-5 * 0)#

#3 = 7x + 0#

#3 = 7x#

#3/color(red)(7) = (7x)/color(red)(7)#

#3/7 = (color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7))#

#3/7 = x#

The x-intercept is: #3/7# or #(3/7, 0)#

y-intercept:

Substitute #0# for #x# and solve for #y#

#3 = (7 * 0) + -5y#

#3 = 0 - 5y#

#3 = -5y#

#3/color(red)(-5) = (-5y)/color(red)(-5)#

#3/-5 = (color(red)(cancel(color(black)(-5)))y)/cancel(color(red)(-5))#

#-3/5 = y#

The y-intercept is: #-3/5# or #(0, -3/5)#