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37 votes
37 votes
What is y-3=3/4(x-5) in standard form?

User Mmatyas
by
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2 Answers

10 votes
10 votes

Answer:


y-3=(3)/(4) (x-5)\\\\y-3=(3)/(4)x-(3)/(4)(5)\\\\y=(3)/(4) x+3-(15)/(4) \\\\y=(3)/(4) x+(12)/(4) -(15)/(4) \\\\y=(3)/(4) x-(3)/(4)

Is this standard form? :\

User Scott Olson
by
3.1k points
19 votes
19 votes

Answer:

3x-4y=3

Explanation:

Hi there!

We are given the equation y-3=
(3)/(4)(x-5), and we want to write it in standard form

Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0

So let's expand the parentheses in the equation

Do the distributive property

y-3=
(3)/(4)x-(15)/(4)

Add 3 to both sides

y=
(3)/(4)x-(3)/(4)

We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

Remember that we want it in standard form, which is ax+by=c

Subtract
(3)/(4)x from both sides


(-3)/(4)x+y=(-3)/(4)

Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative

So multiply both sides by -4


-4((-3)/(4)x+y)=-4((-3)/(4))

Distribute -4 to every number


-4((-3)/(4)x)+-4(y)=-4((-3)/(4))

Multiply


(12)/(4)x-4y=(12)/(4)

Simplify

3x-4y=3

There's the equation in standard form

Hope this helps!

User Ddmps
by
3.0k points