Question

Select all the points that are on the graph of the equation $4y-6x=12$.

• A. $(-4,-3)$
• B. $(-1,1.5)$
• C. $(0,-2)$
• D. $(0,3)$
• E. $(3,4)$
• F. $(6,4)$

Answer 1

Answer: (A), (B), (D)

$(0,3)$

Explanation for correct options:
Putting the points into given equation $4y-6x=12$
Option A : $(-4,-3)$
$$\begin{gathered} \Rightarrow 4y-6x=4(-3)-6(-4) \\ =-12+24 \\ =12 \end{gathered}$$

Option B : $(-1,1.5)$
$$\begin{gathered} \Rightarrow 4y-6x=4(1.5)-6(-1) \\ =6+6 \\ =12 \end{gathered}$$
Option D : $(0,3)$
$$\begin{gathered} \Rightarrow 4y-6x=4\left(3\right)-6\left(0\right) \\ =12+0 \\ =12 \end{gathered}$$

Explanation for incorrect options:
Option C : $(0,-2)$
$$\begin{gathered} \Rightarrow 4y-6x=4(-2)-6\left(0\right) \\ =-8+0 \\ =-8\ne 12 \end{gathered}$$
Option E : $(3,4)$
$$\begin{gathered} \Rightarrow 4y-6x=4\left(4\right)-6\left(3\right) \\ =16-18 \\ =-2\ne 12 \end{gathered}$$
Option F : $(6,4)$
$$\begin{gathered} \Rightarrow 4y-6x=4\left(4\right)-6\left(6\right) \\ =16-36 \\ =-20\ne 12 \end{gathered}$$

Hence, option A, B, D are correct.