x-intercept: Set #y# to #0# and solve for #x#:
#4x - 3y - 6 = 0# becomes:
#4x - (3 * 0) - 6 = 0#
#4x - 0 - 6 = 0#
#4x - 6 = 0#
#4x - 6 + color(red)(6) = 0 + color(red)(6)#
#4x - 0 = 6#
#4x = 6#
#(4x)/color(red)(4) = 6/color(red)(4)#
#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 6/4#
#x = 3/2#
The x-intercept is: #x = 3/2# or #(3/2, 0)#
y-intercept: Set #x# to #0# and solve for #y#:
#4x - 3y - 6 = 0# becomes:
#(4 * 0) - 3y - 6 = 0#
#0 - 3y - 6 = 0#
#-3y - 6 = 0#
#-3y - 6 + color(red)(6) = 0 + color(red)(6)#
#-3y - 0 = 6#
#-3y = 6#
#(-3y)/color(red)(-3) = 6/color(red)(-3)#
#(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = 6/-3#
#y = -2#
The y-intercept is: #y = -2# or #(0, -2)#
