Question

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

Answer 1

`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? :\

Answer 2

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!