Question

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

Answer 1

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:

`ax+by=c`

`ax+by-ax=c-ax`

`by=-ax+c`

divide both sides by

`y=-(a)/(b)x+(c)/(b)`

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

`m=-(a)/(b)`

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

`m=-(a)/(b)`

`m=-(-5)/(2)`

`m=(5)/(2)`

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