Question 74223
find the x- and y-intercept of: 
,
x-3y=-6 and
.
x-4y=-8
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Think about graphing.  If a point of the form (x,y) has a zero value of x, then the y
value has to be on the y-axis.  Similarly, if a point of the form (x,y) has a zero value for
y then the value for x has to be on the x-axis.  
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To demonstrate these two ideas, try plotting the point (0,6) you will see that it lies on 
the y-axis 6 units up from the origin. This is because the x value is zero ... and that 
requires the corresponding value of y to be on the y-axis.  
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Next try plotting the point (3,0). You will go out 3 units on the x-axis but that is 
where you will stay because the corresponding value of y is 0.
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In summary we can say that when x = 0, the corresponding value for y is on the y-axis and
when y = 0, the corresponding value for x is on the x-axis.  
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Now go to the first equation which is:
.
x - 3y = -6
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If we set x equal to zero we will find the corresponding value of y that is on the y-axis.
When x is zero in this equation, the equation is reduced to:
.
-3y = -6
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Dividing both sides by -3 results in y = 2.  So our point is x = 0 and y = 2 or just (0,2) 
and this is on the y-axis which means that it is the y-intercept.
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If we then return to the equation, but this time we set y = 0 the equation reduces to
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x = -6
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because y is equal to 0, this point is on the x-axis as we discussed above.  This point
is (-6,0) which means that it is the x-intercept.  Now you can plot the two points 
(0,2) and (-6,0) and these two points can be connected by a straight line running 
through them, and this line is the graph of the equation x - 3y = -6.
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The same thing can be done with the second equation: x - 4y = -8
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First, set x = 0 and solve the equation for y.  With x = 0 the equation becomes just:
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-4y = -8
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Divide both sides by -4 and you get y = 2.  So the point (0,2) is on the graph.  It is
also on the y-axis and is the y-intercept.
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Then set y = 0 in the equation.  When you do the equation reduces to just:
.
x = -8
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So the point (-8,0), which is on the x-axis is also on the graph and is the x intercept.  
Plot the two points (0,2) and (-8,0) and extend a line through them.  This is the graph 
of this equation.
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Hope this helps you to understand how to get the x and y intercepts from a linear equation.
Just set x equal to zero to get the y intercept and next set y equal to zero to get the 
x intercept.