(b) \( 2 c+3 d=36 \)

Did you know that the equation \( 2c + 3d = 36 \) represents a linear relationship in a two-dimensional space? Each solution to this equation corresponds to a point on a straight line, where \( c \) and \( d \) are the variables. If you were to graph this equation, you'd find all the points where the combination of \( c \) and \( d \) satisfies the equation, forming a line that can be explored for its various intercepts! Now, if you're solving for one variable in terms of the other, a common mistake is to forget to express the other variable clearly. For instance, if you'd like to isolate \( c \), you’d rearrange the equation to \( c = \frac{36 - 3d}{2} \). But beware! It's easy to miss the negative signs or miscalculate, especially if you're working with fractions. Make sure to double-check your arithmetic!