Can I get some help finding the values of A, B and C please? Thanks!

A couple things to note:

We are given the coordinate #(-4,2)# which is just a point in #(x,y)# form

Also, we are told that the line is horizontal which means the slope is #0# meaning the coefficient value of #"A"# must be #0#

So given this information the only choices are either c or d

To determine the coefficients of B and C I would take a guess and substitute the given values and evaluate.

The way to actually do this is that since you are given a point you can substitute that point as #x# and #y# in the equation along with #0# for #"A"#

We Know:

#color(blue)(A=0#

#color(green)(x=-4#

#color(green)(y=2#

So, if we guess choice C

#color(blue)(A)color(green)(x)+color(blue)(B)color(green)(y)=color(blue)(C#

#=>(color(blue)(0))(color(green)(-4))+(color(blue)(1))(color(green)(2))=color(blue)((2))#

#=>0+2=2#

#2=2#

So we validated that the coeffieicents for A,B,C are #0,1,2# respectively

Just so we know we are correct let's try choice d

#=>(color(blue)(0))(color(green)(-4))+(color(blue)(1))(color(green)(2))=color(blue)((-4))#

#=>0+2=-4#

#=>2!=-4#

Therefore c. is the only correct answer

The graph below shows the equation with the correct coefficient values crossing at the given point: