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

$y=-\frac{a}{b}x+\frac{c}{b}$

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

$m=-\frac{a}{b}$

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

$m=-\frac{a}{b}$

$m=-\frac{-5}{2}$

$m=\frac{5}{2}$

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