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Question 28794: HOW DO U DO THIS y=3x + 9 when u are trying to figure out the x and y intercept?
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! HOW DO U DO THIS y=3x + 9 when u are trying to figure out the x and y intercept
Given the general form of equation
Ax+By+C= 0----(1)
How to represent it in the intercept form? is the problem on hand. Right?
The procedure for throwing a given equation to a line in the general form to its intercept form is as follows:
Retain the x and y part on one side and take the constant to the other side.
Ax+By = -C
Divide through out by the constant on the other side so as to get 1 as our constant on that other side.
[A/(-C)]x+[B/(-C)]y = 1
Inorder to make the coefficient of x and y 1 in the nr,write the above as
[1/(-C)/A]x +[1/(-C)/B]y = 1
That is x/[(-C)/A]+y/[(-C)/B] = 1
Now the line is in the standard intercept form
x/a+y/b = 1
where the the x-intercept = a and the y-intercept = b
In the above illustration,the x-intercept = (-C)/A and the y-intercept = (-C)/B
Let us consider two examples one with constant on the LHS negative and the other with the constant on the LHS positive in the general form Ax+By+C=0
1)2x+5y-3 = 0 ----(I)
2x+5y = 3
(2/3)x+(5/3)y =1
x/(3/2)+y/(3/5) = 1
Therefore x-intercept = (3/2) and y-intercept = (3/5)
2)3x+7y+15 = 0 ----(II)
3x +7y =-15
[3/(-15)]x+ [7/(-15)]y =1
x/[(-15)/3]+ y/[(-15)/7]=1
Therefore x-intercept = (-15/3)=-5 and y-intercept = (-15/7)
Coming to your problem
y=3x + 9 which is
3x-y = -9----(1)
(actually the general form is 3x-y+9=0, the C illustrated above is actually 9)
(Got it!. The x and y part are on one side
and the costant part on the other side)
Dividing by (-9) through out
[3/(-9)]x +[(-1)/(-9)]y = 1
[1/(-3)}x +[1/9]y = 1
x/(-3)+y/9 = 1
Therefore x-intercept = (-3) and y - intercept = 9
Verification: Consider the intercept form that we have got.
x/(-3)+y/9 = 1
Multiplying through out by 9,
-3x+y =9
That is y = 3x+9 (adding +3x to both the sides)
Note: After throwing the given equation in the x/a+y/b = 1 form,
the dr under x gives the x-intercept(along with the sign) and
the dr under y gives the y-intercept(along with the sign)
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