To determine which points lie on the graph of the equation [tex]\(4y - 6x = 12\)[/tex], we need to evaluate the equation [tex]\(4y - 6x\)[/tex] for each given point and see if it equals 12.
Let's go through each point step-by-step:
1. Point [tex]\((-4, -3)\)[/tex]:
[tex]\[
4(-3) - 6(-4) = -12 + 24 = 12
\][/tex]
Since [tex]\(4(-3) - 6(-4) = 12\)[/tex], [tex]\((-4, -3)\)[/tex] lies on the graph of the equation.
2. Point [tex]\((-1, 1.5)\)[/tex]:
[tex]\[
4(1.5) - 6(-1) = 6 + 6 = 12
\][/tex]
Since [tex]\(4(1.5) - 6(-1) = 12\)[/tex], [tex]\((-1, 1.5)\)[/tex] lies on the graph of the equation.
3. Point [tex]\((0, -2)\)[/tex]:
[tex]\[
4(-2) - 6(0) = -8 + 0 = -8
\][/tex]
Since [tex]\(4(-2) - 6(0) = -8\)[/tex], [tex]\((0, -2)\)[/tex] does not lie on the graph of the equation.
4. Point [tex]\((0, 3)\)[/tex]:
[tex]\[
4(3) - 6(0) = 12 + 0 = 12
\][/tex]
Since [tex]\(4(3) - 6(0) = 12\)[/tex], [tex]\((0, 3)\)[/tex] lies on the graph of the equation.
5. Point [tex]\((3, -4)\)[/tex]:
[tex]\[
4(-4) - 6(3) = -16 - 18 = -34
\][/tex]
Since [tex]\(4(-4) - 6(3) = -34\)[/tex], [tex]\((3, -4)\)[/tex] does not lie on the graph of the equation.
6. Point [tex]\((6, 4)\)[/tex]:
[tex]\[
4(4) - 6(6) = 16 - 36 = -20
\][/tex]
Since [tex]\(4(4) - 6(6) = -20\)[/tex], [tex]\((6, 4)\)[/tex] does not lie on the graph of the equation.
From this evaluation, the points that lie on the graph of the equation [tex]\(4y - 6x = 12\)[/tex] are:
- [tex]\((-4, -3)\)[/tex]
- [tex]\((-1, 1.5)\)[/tex]
- [tex]\((0, 3)\)[/tex]
Thus, the correct selections are:
A. [tex]\((-4, -3)\)[/tex]
B. [tex]\((-1, 1.5)\)[/tex]
D. [tex]\((0, 3)\)[/tex]
