which relationship has a zero slope?

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. A zero - slope means $y_2 - y_1 = 0$ (i.e., $y$ values are constant).

Step2: Analyze first table

For the first table with points $(-3,2),(-1,2),(1,2),(3,2)$, for any two points say $(x_1,y_1)=(-3,2)$ and $(x_2,y_2)=(-1,2)$, $m=\frac{2 - 2}{-1-(-3)}=\frac{0}{2}=0$.

Step3: Analyze second table

For the second table with points $(-3,3),(-1,1),(1, - 1),(3,-3)$, using two points $(x_1,y_1)=(-3,3)$ and $(x_2,y_2)=(-1,1)$, $m=\frac{1 - 3}{-1-(-3)}=\frac{-2}{2}=-1$.

Step4: Analyze first graph

The first graph is a straight line with a positive slope. If we take two points on the line, say $(0,0)$ and $(1,1)$, $m=\frac{1 - 0}{1 - 0}=1$.

Step5: Analyze second graph

The second graph is a vertical line. For a vertical line, the slope is undefined since the denominator $x_2 - x_1=0$ for any two points on the line.

Answer:

The first table (with $x=-3,-1,1,3$ and $y = 2$ for all $x$ values) has a zero slope.