Question
2x+3y=39 is that linear; function, linear ;not a function, nonlinear 'function, or non linear ;not a function
Answers
GPT-4o mini
The equation \(2x + 3y = 39\) is a linear equation. To determine whether it represents a linear function, we can rearrange it into the slope-intercept form \(y = mx + b\):
1. Solve for \(y\):
\[
3y = 39 - 2x
\]
\[
y = \frac{39 - 2x}{3}
\]
\[
y = -\frac{2}{3}x + 13
\]
This equation clearly represents a straight line in the \(xy\)-plane, which means it is a linear function. Since every \(x\) value produces exactly one \(y\) value, it is also a function.
Therefore, the correct classification of the equation is a **linear function**.
1. Solve for \(y\):
\[
3y = 39 - 2x
\]
\[
y = \frac{39 - 2x}{3}
\]
\[
y = -\frac{2}{3}x + 13
\]
This equation clearly represents a straight line in the \(xy\)-plane, which means it is a linear function. Since every \(x\) value produces exactly one \(y\) value, it is also a function.
Therefore, the correct classification of the equation is a **linear function**.