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Question 468771: Hello Tutors of Algebra.com ,
I just want to ask how to solve this problem ?
3x - 2y = 6x - 3y + 4
how can I change it to standard form ?
how can I change it to slope intercept?
and can you provide solutions so I can understand clearly?
thanks in advance I hope you can answer me
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! equation is 3x - 2y = 6x - 3y + 4
standard form of the equation is ax + by = c
subtract 6x from both sides of the equation to get:
-3x - 2y = -3y + 4
add 3y to both sides of the equation to get:
-3x + y = 4
the equation is now in standard form.
a = -3
b = 1
c = 4
slope intercept form of the equation is y = mx + b where m is the slope and b is the y intercept.
add 3x to both sides of the equation of -3x + y = 4 to get:
y = 3x + 4
the equation is now in slope intercept form.
m = slope = 3
y intercept = value of y when x is equal to 0 = 4
graph of y = 3x + 4 is shown below:
you can plot the values of y for x = 0,1,2 from either the slope intercept form of the equation or the standard form of the equation.
the slope intercept form is easier since it has already solved for y in terms of x.
when x = 0, y = 4
when x = 1, y = 7
when x = 2, y = 10
working from the standard form of the equation, you'll get the same answer.
for example:
when x = 2, the standard form of the equation of -3x + y = 4 becomes -6 + y = 4 which becomes y = 10 after you add 6 to both sides of the equation.
the original form of the equation should also get you the right answer if you converted everything correctly.
the original form of the equation is -3x - 2y = -3y + 4
replacing x with 2, you get:
-6 - 2y = -3y + 4
add 6 to both sides of the equation to get -2y = -3y + 10
add 3y to both sides of the equation to get y = 10
when x = 2, y = 10.
all forms of the equation get you the same value of y for the same value of x as they should.
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