Question

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

Answer 1

C. `A=0,B=1,C=2`

Explanation:

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: