Sketch a graph of each of the following relations. Using the vertical line test, which of these is NOT a function? \( x=0 \) \( 2 x+3 y=6 \) \( y=0 \) \( y=x \)

To visualize the relations: 1. **\( x=0 \)** is a vertical line along the y-axis. 2. **\( 2x + 3y = 6 \)** can be rewritten as \( y = -\frac{2}{3}x + 2 \), which is a straight line with a slope of -2/3. 3. **\( y=0 \)** is the horizontal line along the x-axis. 4. **\( y=x \)** is a diagonal line that passes through the origin at a 45-degree angle. Now, when applying the vertical line test, a vertical line should intersect the graph at most once for it to be a function. The relation \( x = 0 \) fails this test since every point on this line corresponds to multiple y-values, indicating that it is NOT a function! All other relations pass the vertical line test, confirming they are indeed functions. So there you have it! Time to whip out that graph paper and get sketching!