Question

find the slope of the graph and the table. do they have the same slopes? show your work here slope of graph = slope of table = ∘ yes, the slopes are the same. ∘ no, the slopes are not the same. check

Explanation:

Step1: Find slope of graph

Use two points on the line, e.g., \((0, 2)\) and \((2, 6)\). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m = \frac{6 - 2}{2 - 0} = \frac{4}{2} = 2\).

Step2: Find slope of table

Use two points from table, e.g., \((3, -2)\) and \((5, -6)\). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m = \frac{-6 - (-2)}{5 - 3} = \frac{-4}{2} = -2\)? Wait, no—wait, check table again. Wait, table has \(x=3, y=-2\); \(x=5, y=-6\). Wait, maybe I picked wrong points. Wait, let's recalculate. Wait, maybe the graph's slope: let's check another point. Wait, the graph line: when \(x=-1\), \(y=0\); \(x=0\), \(y=2\). So slope is \(\frac{2 - 0}{0 - (-1)} = 2\). Now table: let's take \(x=3, y=-2\) and \(x=5, y=-6\). Wait, \(\frac{-6 - (-2)}{5 - 3} = \frac{-4}{2} = -2\). Wait, that's different? Wait, no, maybe I misread the table. Wait the table: \(x\) values 3,5,6,7,8,10; \(y\) values -2, -6, -8, -10, -12, -16. Wait, let's take \(x=3, y=-2\) and \(x=6, y=-8\). Then slope is \(\frac{-8 - (-2)}{6 - 3} = \frac{-6}{3} = -2\). Wait, but the graph's slope is positive 2, table's is -2. Wait, but maybe I made a mistake in graph. Wait the graph: the line goes from bottom left to top right, so positive slope. Table: as \(x\) increases, \(y\) decreases, so negative slope. So slopes are different. Wait, but let's recheck graph. Let's take two points: when \(x=-1\), \(y=0\); \(x=1\), \(y=4\)? Wait no, the grid: each square is 1 unit? Let's see, the line passes through (0,2) and (2,6): rise 4, run 2, slope 2. Table: from x=3 to x=5, y goes from -2 to -6: decrease by 4, run 2, slope -2. So slope of graph is 2, slope of table is -2. So they are not the same.

Wait, but maybe I messed up the table's y-values. Wait the table: x=3, y=-2; x=5, y=-6. So change in y: -6 - (-2) = -4; change in x: 5 - 3 = 2; slope -2. Graph: change in y: 6 - 2 = 4; change in x: 2 - 0 = 2; slope 2. So slopes are 2 and -2, so not same.

Answer:

Slope of graph = \(2\)
Slope of table = \(-2\)
No, the slopes are not the same.