Question

sal has created a recipe for a dry, packaged cookie dough mix. only coconut milk needs to be added to the dry mix to make the dough, which is then baked. sal already has 200 grams of dough made with the mix and the coconut milk, but wants to make more. for every gram of dry ingredients ( x ) added, 1.2 grams of coconut milk is added to produce ( y ) total grams of dough. in slope intercept form, the equation describing this situation is ( y = 1.2x + 200 ). what is the standard form of the equation that models the amount of dough that sal might make in this batch?
( 5x + 6y = 1,000 )
( 6x + 5y = 1,000 )
( 6x - 5y = -1,000 )
( -5x + 6y = 1,000 )

Explanation:

Step1: Start with given slope-intercept form

$y = 1.2x + 200$

Step2: Eliminate decimal coefficient

Multiply all terms by 10: $10y = 12x + 2000$

Step3: Rearrange to standard form $Ax+By=C$

Subtract $12x$ from both sides: $-12x + 10y = 2000$

Step4: Simplify by dividing by 2

$\frac{-12x}{2} + \frac{10y}{2} = \frac{2000}{2}$ which gives $-6x + 5y = 1000$, or multiply by -1 to match the option: $-5x + 6y = 1000$

Answer:

$-5x + 6y = 1,000$