Question 29630
to find the x-intercept ... solve for x
{{{ x = ym +- b }}}  this is the same formula as the point slope form of {{{ y = mx +- b }}}
where in both cases, b is the x-intercept or y-intercept.

{{{ x - y = -6 }}} add y to both sides
{{{ x = y - 6 }}} -6 is it x-int.

next problem
{{{ x - 3y = 7 }}}  add 3y to both sides
{{{ x  = + 3y + 7 }}} +7 is the x-inter

next ...
{{{ -3+y=15 }}} there is no x ... this is a horizontal line. solve for y. Add 3 to both sides
{{{ y = 15 + 3 }}} add
{{{ y = 18 }}} Since y is not equal to 0, the line does not touch the x-axis

next ...
here is a short cut without having to solve the WHOLE equation.
{{{ 6x + 12y = 36 }}} look at the x value and the constant ...
{{{ highlight(6x) + 12y = highlight(36) }}} work only that portion ...
{{{ 6x = 36 }}} divide both sides by 6
{{{ x = 6 }}} this is the x intercept

next ... do the same on the last one.
{{{ 2x-10y=-30 }}}
{{{ highlight(2x)-10y=highlight(-30) }}}
{{{ 2x=-30 }}} divide by 2
{{{ x = -15 }}}