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:
[tex]ax+by=c[/tex]
[tex]ax+by-ax=c-ax[/tex]
[tex]by=-ax+c[/tex]
divide both sides by
[tex]y=-\frac{a}{b}x+\frac{c}{b}[/tex]
Now compare it with y=mx+b, we get
[tex]m=-\frac{a}{b}[/tex]
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
[tex]m=-\frac{a}{b}[/tex]
[tex]m=-\frac{-5}{2}[/tex]
[tex]m=\frac{5}{2}[/tex]
Now matching these details with given choices we find that THIRD choice is the final answer.
