Plot the points that are given in the table below, where time (in seconds) represents your x-axis and displacement (in meters) represents your y-axis. Once you have plotted your graph, determine the value of the slope.
Time (s) Displacement (m)
2 21
4 35
5 42
9 70
First, we plot the points on a coordinate plane:
(2, 21), (4, 35), (5, 42), (9, 70)
Next, we can determine the slope of the line passing through these points using the slope formula:
slope = (change in y) / (change in x)
We can choose any two points to calculate the slope. Let's use (2, 21) and (9, 70):
slope = (70 - 21) / (9 - 2) = 49 / 7
Therefore, the slope of the line passing through the given points is 7.
Plot the points that are given in the table below, where time (in seconds) represents your -axis and displacement (in meters) represents your -axis. Once you have plotted your graph, determine the value of the slope.
Time (s) Displacement (m)
0 3
4 27
7 45
8 51
First, we plot the points on a coordinate plane:
(0, 3), (4, 27), (7, 45), (8, 51)
Next, we can determine the slope of the line passing through these points using the slope formula:
slope = (change in y) / (change in x)
We can choose any two points to calculate the slope. Let's use (0, 3) and (8, 51):
slope = (51 - 3) / (8 - 0) = 48 / 8 = 6
Therefore, the slope of the line passing through the given points is 6.
To plot the points and determine the slope, you can follow these steps:
1. Set up a coordinate system with the x-axis representing time (s) and the y-axis representing displacement (m).
2. Plot the given points on the graph. For each data point, locate the corresponding time value on the x-axis and the displacement value on the y-axis, then mark the point.
3. After plotting all the points, you should have four points on the graph: (2, 21), (4, 35), (5, 42), and (9, 70).
4. Draw a straight line connecting the points on the graph. This line represents the relationship between time and displacement.
5. To determine the slope of the line, choose any two points on the line. Let's take points (2, 21) and (9, 70).
6. Calculate the change in displacement and change in time between the two points:
Change in displacement = 70 - 21 = 49m
Change in time = 9 - 2 = 7s
7. Now, calculate the slope using the formula:
Slope = Change in displacement / Change in time
Slope = 49m / 7s = 7 m/s
The value of the slope is 7 m/s. This means that for every second passed, the displacement increases by 7 meters.