To determine the point at which the graph of the equation [tex]\(5x - 3y + 2 = 0\)[/tex] crosses the [tex]\(y\)[/tex]-axis, we need to find the [tex]\(y\)[/tex]-coordinate when [tex]\(x = 0\)[/tex].
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[ 5(0) - 3y + 2 = 0 \][/tex]
This simplifies to:
[tex]\[ -3y + 2 = 0 \][/tex]
2. Solve for [tex]\(y\)[/tex]:
Subtract 2 from both sides of the equation:
[tex]\[ -3y = -2 \][/tex]
Then, divide both sides by [tex]\(-3\)[/tex]:
[tex]\[ y = \frac{-2}{-3} = \frac{2}{3} \][/tex]
Thus, the coordinates where the graph crosses the [tex]\(y\)[/tex]-axis are [tex]\((0, \frac{2}{3})\)[/tex].
Therefore, the correct answer is:
D) [tex]\(\left(0, \frac{2}{3}\right)\)[/tex].
