The temperatures at 10pm were 58f outside and 67f inside. At 4am they were 48f outside and 62f inside. Draw a graph of these data points and calculate slope of the line connecting them.
Since the time elapsed is 6 hours, the slopes are
(48-58)/6 and (62-67)/6
To draw a graph of the data points, we'll use temperature as the y-axis and time as the x-axis. The given data points are as follows:
(10pm, 58°F outside, 67°F inside)
(4am, 48°F outside, 62°F inside)
The x-axis represents time, and the y-axis represents temperature in degrees Fahrenheit.
1. Plot the first data point: At 10pm, the outside temperature was 58°F, so plot a point at (10, 58) on the graph.
2. Plot the second data point: At 10pm, the inside temperature was 67°F, so plot a point at (10, 67) on the graph.
3. Plot the third data point: At 4am, the outside temperature was 48°F, so plot a point at (4, 48) on the graph.
4. Plot the fourth data point: At 4am, the inside temperature was 62°F, so plot a point at (4, 62) on the graph.
Connect the two points to form a line on the graph.
To calculate the slope of the line connecting the two data points, you can use the formula:
Slope (m) = (change in y) / (change in x)
In our case, (change in y) is the difference in inside temperatures, and (change in x) is the difference in time.
(change in y) = 62 - 67 = -5
(change in x) = 4 - 10 = -6
Slope (m) = (-5) / (-6) = 5/6
Therefore, the slope of the line connecting the two data points is 5/6.
To draw a graph of the given data points and calculate the slope of the line connecting them, follow these steps:
1. On a graph paper or using a graphing tool, draw a set of x and y-axis. Label the x-axis as time (in hours) and the y-axis as temperature (in Fahrenheit).
2. Plot the first data point (10pm) at (0, 58) where the x-value represents the time (0 hours) and the y-value represents the temperature at that time (58°F). Plot the second data point (4am) at (6, 48) where the x-value represents the time (6 hours) and the y-value represents the temperature at that time (48°F).
3. Connect the two plotted points with a straight line. Make sure the line passes through both points.
4. Calculate the slope of the line using the formula: slope = (change in y) / (change in x). In this case, the change in y is the difference in temperatures (67 - 48 = 19°F) and the change in x is the difference in time (6 - 0 = 6 hours). Therefore, the slope is 19°F / 6 hours, which simplifies to approximately 3.17°F/hour.
Remember to label your graph with appropriate units and a title to make it clear what the data represents.