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# Sketch a contour diagram for the function with at least four labeled contours. Describe in words the contours and how they are spaced. f(x, y)=3x+3y

Solution

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The contorus of the given function ${\color{#4257b2}f(x,y)=C}$ are lines with slope equal to $-1$.

Equation of the line ${\color{#4257b2}f(x,y)=C}$ is:

$\boxed{{\color{#4257b2}3x+3y=C}}$

This is a equation of a line with itercepts ${\color{#4257b2}x=\dfrac{C}{3}}$ and ${\color{#4257b2}y=\dfrac{C}{3}}$.

As we can see at the pictures above, the function ${\color{#4257b2}f(x,y)}$ is increasing function of $y$ and $x$.

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