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…

Explanation:

Step1: Rearrange the equation

Given $4y - 6x=12$, we can express $y$ in terms of $x$ as $y=\frac{6x + 12}{4}=\frac{3x}{2}+ 3$.

Step2: Check point A $(-4,-3)$

Substitute $x = - 4$ into $y=\frac{3x}{2}+3$. Then $y=\frac{3\times(-4)}{2}+3=-6 + 3=-3$. So point A is on the graph.

Step3: Check point B $(-1,1.5)$

Substitute $x=-1$ into $y=\frac{3x}{2}+3$. Then $y=\frac{3\times(-1)}{2}+3=-\frac{3}{2}+3=\frac{-3 + 6}{2}=1.5$. So point B is on the graph.

Step4: Check point C $(0,-2)$

Substitute $x = 0$ into $y=\frac{3x}{2}+3$. Then $y=\frac{3\times0}{2}+3=3\neq - 2$. So point C is not on the graph.

Step5: Check point D $(0,3)$

Substitute $x = 0$ into $y=\frac{3x}{2}+3$. Then $y=\frac{3\times0}{2}+3=3$. So point D is on the graph.

Step6: Check point E $(3,-4)$

Substitute $x = 3$ into $y=\frac{3x}{2}+3$. Then $y=\frac{3\times3}{2}+3=\frac{9}{2}+3=\frac{9 + 6}{2}=\frac{15}{2}\neq-4$. So point E is not on the graph.

Step7: Check point F $(6,4)$

Substitute $x = 6$ into $y=\frac{3x}{2}+3$. Then $y=\frac{3\times6}{2}+3=9 + 3=12\neq4$. So point F is not on the graph.

Answer:

A. $(-4,-3)$ B. $(-1,1.5)$ D. $(0,3)$