To find the value of [tex]\(a\)[/tex] for the point [tex]\((a, 2)\)[/tex] that lies on the graph of the equation [tex]\(2x - 3y + 8 = 0\)[/tex], follow these steps:
1. Substitute the y-coordinate into the equation: Given the point [tex]\((a, 2)\)[/tex], we know that [tex]\(y = 2\)[/tex]. Substitute [tex]\(y = 2\)[/tex] into the equation [tex]\(2x - 3y + 8 = 0\)[/tex]:
[tex]\[
2x - 3(2) + 8 = 0
\][/tex]
2. Simplify the equation: Perform the multiplication and addition operations within the equation:
[tex]\[
2x - 6 + 8 = 0
\][/tex]
3. Combine like terms: Combine the constant terms [tex]\(-6\)[/tex] and [tex]\(8\)[/tex]:
[tex]\[
2x + 2 = 0
\][/tex]
4. Solve for [tex]\(x\)[/tex]: Isolate [tex]\(x\)[/tex] by moving the constant term to the other side of the equation:
[tex]\[
2x = -2
\][/tex]
5. Divide by the coefficient of [tex]\(x\)[/tex]: Solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{-2}{2}
\][/tex]
[tex]\[
x = -1
\][/tex]
Therefore, the value of [tex]\(a\)[/tex] is [tex]\(-1\)[/tex]. So, the point [tex]\((a, 2)\)[/tex] that lies on the graph of the given equation has [tex]\(a = -1\)[/tex].
