Question 384149
Perhaps the problem should be
3x - 4y = 12.
Put it in the slope/intercept form which is y = mx + b, where m=slope, b=y intercept
subtract 3x from both sides
-4y = -3x + 12
y has to be positive, multiply both sides by -1
4y = +3x - 12
The coefficient of y has to be 1, divide both sides by 4
y = {{{3/4}}}x - {{{12/4}}}
y = {{{3/4}}}x - 3
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the y intercept occurs when x=0, replace x with 0, and find y
y = {{{3/4}}}(0) - 3
y = 0 - 3
y = -3, is the y intercept 
The ordered pair to graph this; x=0, y=-3
:
The x intercept occurs when y = 0, write it like this, and solve for x
{{{3/4}}}x - 3 = 0; (replacing y with 0)
Add 3 to both sides
{{{3/4}}}x = +3
multiply both sides by 4, to get rid of the fraction
3x = 4(3)
3x = 12
Divide both sides by 3
x = {{{12/3}}}
x = 4; is the x intercept
the ordered pair to graph this: x=4, y=0
:
Graphically it should be apparent
{{{ graph( 300, 300, -10, 10, -10, 10, .75x-3) }}}
You can see the line intercepts the y axis at -3
and the x axis at +4
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How about it, did this shed some lite on this "intercept stuff" for you?