Question

find the slope of the table and the graph. do they have the same slopes?
x 1 2 3 4 6 7 8
y 5 9 13 17 25 29 33
draw
slope of table =
slope of graph =
yes, the slopes are the same.
no, the slopes are not the same.

Explanation:

Step1: Calculate slope of table

Use slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Take points (1,5) and (2,9):
\( m_{table} = \frac{9 - 5}{2 - 1} = \frac{4}{1} = 4 \).

Step2: Calculate slope of graph

Identify two points on graph: (0,2) and (1,3) (or (1,3) and (2,4), etc.).
\( m_{graph} = \frac{3 - 2}{1 - 0} = \frac{1}{1} = 1 \)? Wait, no—wait, recheck graph. Wait, the graph has points: when x=0, y=2; x=1, y=3? Wait, no, looking at the graph, the blue dots: one at (0,2), one at (1,3)? Wait, no, maybe (0,2) and (2,4). Then \( m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1 \)? Wait, no, earlier table slope was 4. Wait, maybe I misread the graph. Wait, the table: x=1, y=5; x=2, y=9 (difference 4 in y, 1 in x: slope 4). The graph: let's check coordinates. The y-axis has 2,4,6,8. The line passes through (0,2) and (2,4)? Wait, no, the blue dot at (1,3)? Wait, no, the first blue dot is at (0,2), then next at (1,3)? Wait, no, maybe the graph's slope is 1, but table's is 4. Wait, no, maybe I made a mistake. Wait, table: x=1, y=5; x=2, y=9: Δy=4, Δx=1, slope 4. Graph: let's take two points. Let's see, the line goes through (0,2) and (1,3)? No, wait, the y-intercept is 2, and the next point: when x=1, y=3? But then slope is 1. But table's slope is 4. So slopes are different. Wait, but maybe I misread the graph. Wait, the graph's y-axis: the numbers are 2,4,6,8. Wait, maybe the points are (0,2) and (2,6)? No, the line is blue, going up. Wait, let's recalculate table slope again. Take x=1, y=5; x=3, y=13: Δy=8, Δx=2, slope 4. Correct. Graph: let's take (0,2) and (1,3): slope 1. So table slope 4, graph slope 1. So they are not the same.

Wait, but maybe I messed up the graph. Wait, the problem's graph: let's check the coordinates. The x-axis: -8 to 8, y-axis: -4 to 8. The line passes through (0,2) and (2,4)? Then slope is (4-2)/(2-0)=1. Table slope is 4. So slopes are different.

Answer:

Slope of table = \( 4 \)
Slope of graph = \( 1 \)
No, the slopes are not the same.

(Wait, but maybe I misread the graph. Wait, maybe the graph's points are (0,2) and (1,6)? No, the y-axis is marked 2,4,6,8. Wait, the first blue dot is at (0,2), then next at (1,6)? No, that can't be. Wait, maybe the graph is different. Wait, the table: x=1, y=5; x=2, y=9 (slope 4). The graph: let's see, if the line has slope 4, then from (0,2), next point would be (1,6), (2,10), but the graph's y-axis only goes up to 8. So maybe the graph's slope is 1, table's is 4. So the answer is:

Slope of table = 4
Slope of graph = 1
No, the slopes are not the same.