To determine on which side of the line [tex]\(5x - 4y + 6 = 0\)[/tex] the points [tex]\((0, 0)\)[/tex] and [tex]\((-1, 3)\)[/tex] lie, we need to substitute each point into the equation of the line and evaluate the result.
### Checking Point [tex]\((0, 0)\)[/tex]:
1. Substitute [tex]\(x = 0\)[/tex] and [tex]\(y = 0\)[/tex] into the equation [tex]\(5x - 4y + 6 = 0\)[/tex]:
[tex]\[
5(0) - 4(0) + 6 = 0 \implies 0 - 0 + 6 = 6
\][/tex]
2. The result is [tex]\(6\)[/tex], which is positive. This means that the point [tex]\((0, 0)\)[/tex] lies above the line [tex]\(5x - 4y + 6 = 0\)[/tex].
### Checking Point [tex]\((-1, 3)\)[/tex]:
1. Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 3\)[/tex] into the equation [tex]\(5x - 4y + 6 = 0\)[/tex]:
[tex]\[
5(-1) - 4(3) + 6 = 0 \implies -5 - 12 + 6 = -11
\][/tex]
2. The result is [tex]\(-11\)[/tex], which is negative. This means that the point [tex]\((-1, 3)\)[/tex] lies below the line [tex]\(5x - 4y + 6 = 0\)[/tex].
### Conclusion:
- The point [tex]\((0, 0)\)[/tex] lies above the line [tex]\(5x - 4y + 6 = 0\)[/tex].
- The point [tex]\((-1, 3)\)[/tex] lies below the line [tex]\(5x - 4y + 6 = 0\)[/tex].
