Which answer choice explains the pattern for how to find the slope using an equation in standard form?

Question is using standard formula ax+by=c to find the slope by converting into slope intercept form y=mx+b

so we also need to convert ax+by=c into y=mx+b as shown below:

divide both sides by

Now compare it with y=mx+b, we get

So using values of a and b, we can find the slope

compare given equation -5x+2y=15 with ax+by=c, we get:

a=-5, b=2

Now plug both into above formula

Now matching these details with given choices we find that THIRD choice is the final answer.

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)