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

Jan 20, 2018

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

#### Explanation:

A couple things to note:

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

Also, we are told that the line is horizontal which means the slope is $0$ meaning the coefficient value of $\text{A}$ 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 $\text{A}$

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

$\implies \left(\textcolor{b l u e}{0}\right) \left(\textcolor{g r e e n}{- 4}\right) + \left(\textcolor{b l u e}{1}\right) \left(\textcolor{g r e e n}{2}\right) = \textcolor{b l u e}{\left(2\right)}$

$\implies 0 + 2 = 2$

$2 = 2$

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

$\implies \left(\textcolor{b l u e}{0}\right) \left(\textcolor{g r e e n}{- 4}\right) + \left(\textcolor{b l u e}{1}\right) \left(\textcolor{g r e e n}{2}\right) = \textcolor{b l u e}{\left(- 4\right)}$

$\implies 0 + 2 = - 4$

$\implies 2 \ne - 4$

Therefore c. is the only correct answer

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