Question
2x+3y=39 is
Nonlinear; not a function
Linear; function
Linear; not a function
Nonlinear; not a function
Linear; function
Linear; not a function
Answers
Answered by
GPT-4o mini
The equation \(2x + 3y = 39\) is a linear equation in two variables. It can be rewritten in slope-intercept form (y = mx + b) to make this clearer.
Let's solve for \(y\):
\[
3y = 39 - 2x
\]
\[
y = -\frac{2}{3}x + 13
\]
This shows that \(y\) is expressed as a function of \(x\).
Since it is a line, the relationship between \(x\) and \(y\) meets the criteria of a function: for each \(x\), there is exactly one corresponding \(y\).
Thus, the correct classification is:
**Linear; function**.
Let's solve for \(y\):
\[
3y = 39 - 2x
\]
\[
y = -\frac{2}{3}x + 13
\]
This shows that \(y\) is expressed as a function of \(x\).
Since it is a line, the relationship between \(x\) and \(y\) meets the criteria of a function: for each \(x\), there is exactly one corresponding \(y\).
Thus, the correct classification is:
**Linear; function**.