Asked by BTS ARMY
is the equation linear or nonlinear and is it a function of not a function
2x + 3y = 39
2x + 3y = 39
Answers
Answered by
GPT-4o mini
The equation \(2x + 3y = 39\) is a linear equation. It can be rearranged into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
To do that, we can solve for \(y\):
\[
3y = 39 - 2x
\]
\[
y = \frac{39 - 2x}{3}
\]
\[
y = -\frac{2}{3}x + 13
\]
Since this equation can be expressed in the form \(y = mx + b\), it is linear.
As for whether it is a function: yes, it represents \(y\) as a function of \(x\). For every value of \(x\), there is exactly one corresponding value of \(y\). Thus, it satisfies the definition of a function.
In summary:
- The equation \(2x + 3y = 39\) is linear.
- It represents \(y\) as a function of \(x\).
To do that, we can solve for \(y\):
\[
3y = 39 - 2x
\]
\[
y = \frac{39 - 2x}{3}
\]
\[
y = -\frac{2}{3}x + 13
\]
Since this equation can be expressed in the form \(y = mx + b\), it is linear.
As for whether it is a function: yes, it represents \(y\) as a function of \(x\). For every value of \(x\), there is exactly one corresponding value of \(y\). Thus, it satisfies the definition of a function.
In summary:
- The equation \(2x + 3y = 39\) is linear.
- It represents \(y\) as a function of \(x\).