Question 491974: We had a seat work in class in which the instructions was to write an equation of a linear function given the following conditions:
the first was Given a slope and intercept..
My final answer was in the form y= mx + b but my teacher made it wrong. she told us that it must be in the form ax + by = c. I scanned my notes to make sure that what i am telling is right. I found out that my teacher gave us a seatwork in whch the given equations were in the form y= mx + b and the instructions was " Rewrite the following linear functions in standard form."
Please help me, what should I do? Are my answers correct or wrong?
Found 2 solutions by Theo, richard1234:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the slope intercept form of a linear equation is y = mx + b
the standard form of a linear equation is ax + by = c
suppose your equation was:
2x + 3y = 15
that's in standard form with a = 2 and b = 3 and c = 15
subtract 2x from both sides of the equation to get:
3y = -2x + 15
divide both sides of the equation by 3 to get:
y = (-2/3)x + 15/3 which becomes:
y = (-2/3)x + 5
that's the slope intercept form of the equation.
the slope intercept form is y = mx + b
m is the slope and b is the y-intercept.
in this equation, the slope is equal to (-2/3) and the y-intercept is equal to 5.
to convert back to the standard form of the equation, do the following:
you start from y = (-2/3)x + 5
add (-2/3)x to both sides of the equation to get:
(2/3)x + y = 5
multiply both sides of the equation by 3 to get:
2x + 3y = 15
you're back to the standard form of your equation.
these forms are equivalent.
2x + 3y = 15 is equivalent to y = -(2/3)x + 5
just supply a random value for x and solve for y in both equations.
let x = 3.
2x + 3y = 15 becomes 6 + 3y = 15 which becomes 3y = 9 which becomes y = 3.
y = (-2/3)x + 5 becomes y = (-2/3)*3 + 5 which becomes y = -2 + 5 which becomes y = 3.
you get y = 3 in both cases, confirming the fact that the 2 equations are equivalent.
any other value of x will confirm the same.
for example:
when x = 20, 2x + 3y = 15 becomes 40 + 3y = 15 which becomes 3y = -25 which becomes y = -25/3
y = (-2/3)x + 5 becomes y = (-2/3)*20 + 5 which becomes y = -40/3 + 5 which becomes y = -40/3 + 15/3 which becomes -25/3.
y is the same value in both equations, confirming again that the equations are equivalent.
just follow the steps to convert from the slope intercept form of the equation to the standard form of the equation and you should be ok.
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! The slope-intercept form (i.e. y = mx+b) is perfectly valid, but if your instructor wants you to write it in standard form, you should do it. Simply move the mx to the other side to get
-mx + y = b
If your coefficients are rational but not integers, you should multiply both sides by some constant to make the coefficients integers.
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