To determine whether the equation [tex]\(4x + 9y = 36\)[/tex] defines [tex]\(y\)[/tex] as a function of [tex]\(x\)[/tex], we need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex].
Given the equation:
[tex]\[4x + 9y = 36\][/tex]
Follow these steps to solve for [tex]\(y\)[/tex]:
1. Isolate [tex]\(y\)[/tex]: Start by isolating the term involving [tex]\(y\)[/tex] on one side of the equation.
[tex]\[9y = 36 - 4x\][/tex]
2. Solve for [tex]\(y\)[/tex]: Divide both sides of the equation by 9 to solve for [tex]\(y\)[/tex].
[tex]\[y = \frac{36 - 4x}{9}\][/tex]
3. Simplify the expression: Simplify the fraction if possible.
[tex]\[y = \frac{36}{9} - \frac{4x}{9}\][/tex]
[tex]\[y = 4 - \frac{4x}{9}\][/tex]
Thus, we have found that:
[tex]\[y = 4 - \frac{4x}{9}\][/tex]
Since we successfully isolated and solved for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex], the equation does indeed define [tex]\(y\)[/tex] as a function of [tex]\(x\)[/tex]. The function can be written as:
[tex]\[y = 4 - \frac{4x}{9}\][/tex]
